[seqfan] Re: Forbidden digits =2016

Lars Blomberg larsl.blomberg at comhem.se
Mon Dec 21 19:52:38 CET 2015


Hello, 

I find the first 1000 terms to be:
5, 79, 455, 7379, 47955, 7389, 77595, 5843, 78545, 43, 895, 49, 795, 93, 845, 53, 735, 4753, 79835, 9953, 35, 953, 3545, 94343, 353495, 943, 7845, 739, 4855, 939, 4845, 743, 45, 753, 7835, 45753, 7735, 49753, 9735, 48853, 8895, 449, 7895, 443, 8545, 45343, 738495, 5343, 83395, 453, 7395, 45943, 738845, 9933, 38845, 8893, 95, 353, 94435, 353553, 94345, 353443, 94895, 378943, 8954895, 4953, 78435, 553, 7945, 439, 77345, 457533, 97345, 347993, 95795, 353749, 9593795, 89, 3795, 89549, 3895, 85583, 859795, 85783, 388595, 993, 8445, 45393, 9595, 34793, 958795, 83, 4795, 783, 4595, 843, 44595, 883, 8595, 389, 8955, 379, 9355, 489, 7955, 979, 4555, 779, 4955, 879, 55, 789, 54955, 889, 37995, 9843, 34995, 9883, 35995, 9889, 35955, 9979, 33455, 99954379, 35555, 937799, 4899555, 88779, 955, 3539, 945, 3553, 93835, 5953, 73535, 483953, 99895, 333849, 998455995, 37853, 9895, 33849, 9859895, 33949, 9855795, 38949, 895395, 37949, 8839495, 8993, 38445, 895939, 3845, 893, 8845, 39, 855, 8589, 38955, 9589, 349855, 95879, 349955, 95379, 355, 94489, 3995, 83443, 474545, 9453, 395, 8443, 39545, 9833, 44745, 8593, 45895, 7843, 49595, 7783, 49795, 7583, 49895, 749443, 44545, 749343, 99545, 339, 983445, 493, 8995, 483, 9395, 35953, 9835, 48753, 795745, 99, 745, 4743, 74845, 9939, 33945, 9839, 49755, 8839, 44755, 839, 4755, 74739, 783855, 5739, 588855, 9739, 34755, 9738839, 5945, 73993, 479445, 74999, 445, 7493, 995, 3453, 979895, 3443, 974545, 399, 8455, 39479, 844955, 4479, 74455, 9999, 74445, 784399, 4455, 74879, 773855, 5879, 77455, 999, 7445, 47493, 748445, 5339, 74545, 5333, 83545, 933, 47545, 799, 44555, 753979, 5955, 73779, 484555, 73879, 479955, 7479, 79955, 4939, 78445, 7393, 595, 7983, 435595, 7883, 47995, 7489, 78455, 479, 74855, 4739, 755, 44739, 748755, 4994739, 888855, 4989, 89955, 3779, 93555, 3789, 89595, 3783, 935595, 37783, 899595, 383, 87595, 8389, 47495, 7343, 488545, 8953, 435, 7953, 545, 7339, 48445, 7399, 77545, 5899, 77945, 499, 74945, 473393, 83945, 593, 7345, 539, 8345, 533, 73845, 4533, 784345, 4443, 75345, 498433, 8895345, 43593, 889795, 4983, 89495, 3953, 84895, 583, 7795, 749, 47795, 949, 37395, 897943, 39845, 8533, 585345, 9543, 35395, 9449, 78895, 983, 3495, 95389, 349495, 95983, 348495, 97383, 347595, 9893, 37945, 895899, 48955, 734499, 7999955, 494489, 7955355, 433489, 7944455, 9489, 35355, 943979, 3555, 93779, 484955, 899, 3955, 84389, 9455, 35479, 957855, 37479, 895855, 97989, 555, 7889, 45455, 8439, 47345, 735993, 48745, 9793, 34595, 9753853, 5995, 79883, 4355595, 79983, 9495, 39389, 848955, 4589, 73955, 589, 83955, 5479, 79455, 4379, 78955, 5489, 79355, 5539, 88355, 8979, 38355, 895539, 3849945, 98439, 389945, 85893, 3945, 84499, 8945, 38499, 894945, 4899, 79555, 4889, 89455, 5989, 577455, 8379, 88955, 5379, 74355, 4489, 88995, 4449, 79995, 4849, 794895, 4949, 89795, 383583, 93459795, 37983, 8939495, 5983, 93595, 379783, 88997795, 549, 79395, 4453, 75395, 4483, 748995, 9853, 37895, 895853, 38995, 855443, 4545, 833, 54545, 733339, 4744545, 9399, 78555, 5789, 579955, 7579, 577355, 7758439, 45735455, 7597989, 735455, 7989, 495, 7949, 49495, 787949, 45495, 8349, 537495, 9949, 77895, 5583, 79795, 473583, 7359795, 75783, 759795, 77593, 757795, 75983, 498595, 793, 43945, 793593, 44795, 8583, 38895, 8843, 88595, 4893, 78845, 733, 538845, 9943, 33545, 9939943, 9845, 34493, 9995, 34453, 9738995, 38453, 935, 4853, 73735, 459753, 77735, 495753, 87735, 853, 8745, 38593, 8744745, 9593, 34795, 9983, 33595, 9953783, 3595, 989, 4495, 74389, 773955, 4579, 94955, 579, 8355, 44979, 8555, 44879, 748555, 4779, 739555, 45889, 738595, 5889, 593555, 7745779, 45798555, 84879, 394555, 84779, 9955, 33589, 9953955, 3389, 989955, 3889, 85995, 3893, 85945, 3939, 84945, 393, 8495, 39383, 849595, 39783, 893595, 39993, 9345, 47993, 737345, 7539, 77445, 5939, 79945, 4439, 75455, 457989, 75495, 473353, 7385395, 48453, 737535, 4738453, 95935, 399853, 85895, 9849, 75895, 457843, 75545, 457933, 7397545, 45953, 8395, 543, 73395, 4543, 74345, 475553, 73345, 4553, 73435, 474553, 7459345, 78543, 475395, 74453, 474895, 9443, 78995, 9493, 88945, 5493, 79845, 4493, 75445, 7893, 47445, 737399, 4737455, 8399, 47455, 7879, 49955, 7779, 45955, 7789, 49555, 7979, 47355, 747439, 4788345, 747393, 47945, 7499, 49945, 747493, 98395, 343, 97545, 345953, 99395, 337943, 987547545, 8453, 44895, 8543, 85845, 388543, 8945845, 3733, 95845, 3543, 95395, 349493, 95445, 3493, 954995, 3533483, 9474344395, 3943, 84845, 398939, 88845, 8733, 388845, 8939, 38545, 894943, 39495, 8983, 38795, 8734593, 9795, 34593, 9754745, 3833, 93545, 3799, 893545, 3843, 873895, 4549, 78795, 9993, 73445, 475939, 7458855, 78939, 9445, 35399, 9545, 34933, 9553545, 35939, 938945, 4839, 79755, 4355839, 89533945, 55839, 883755, 3999739, 843755, 3955839, 84393945, 44493, 753995, 44483, 749395, 44549, 793395, 5543, 78395, 7443, 537345, 8539, 44945, 744899, 7834545, 43333, 78354545, 44343, 754545, 4433, 84545, 394333, 8459545, 87899, 5545, 78339, 457445, 77339, 4457445, 87439, 397345, 87543, 3858395, 89349, 445395, 8949, 89395, 4349, 779395, 58449, 834895, 3993, 83495, 5383, 84595, 3989, 83855, 459589, 74955, 4789, 738955, 48499, 898945, 54893, 799445, 44399, 799545, 49333, 7799545, 47943, 747545, 7939, 49545, 7943, 435545, 8853, 39935, 834853, 39995, 834443, 45395, 8493, 445995, 8483, 589395, 8449, 448995, 99853, 339895, 98393549, 384943895, 995983, 3389495, 98349, 339495, 99953, 334495, 998398943, 399395, 98549, 348795, 98593, 338745, 98853, 348745, 95739, 3755, 89839, 9945, 33539, 9944955, 3479, 95855, 348939, 9855, 33879, 9843555, 34879, 958555, 34779, 9739955, 35779, 943555, 3534399, 954445, 34939, 9543945, 4593, 73895, 4843, 73995, 459483, 7394395, 53349, 934495, 9389, 48455, 9379, 37955, 9479, 39455, 8479, 39955, 8499, 879955, 54939, 788845, 49893, 7595, 45793, 837595, 5893, 73945, 5393, 83345, 474593, 74745, 783833, 4573545, 783799, 55555, 783789, 5555, 78379, 4458955, 79379, 477955, 79479, 5455, 79439, 495455, 77879, 7555, 45789, 733555, 53779, 889555, 3979, 89355, 4979, 89555, 3879, 89855, 383879, 8955555, 44379, 753455, 4744489, 755355, 4578489, 775355, 58489, 775455, 4958379, 785455, 57979, 835455, 9439, 78345, 7593, 439745, 7933593, 4895, 78443, 457395, 75943, 457545, 78343, 757545, 75843, 4398545, 79343, 5495, 79989, 5595, 77853, 5895, 73543, 474345, 73553, 799945, 44439, 753345, 44433, 7955345, 44443, 754895, 44453, 753545, 44853, 743535, 4754953, 79495, 474943, 74395, 5349, 74495, 474983, 7974495, 9349, 38395, 895543, 48895, 735443, 58995, 775453, 9535, 39853, 9935, 45853, 749735, 4587753, 945735, 3753, 94745, 358593, 99795, 338549, 984598795, 339793, 98393945, 3839, 873755, 8874739, 38959845, 997939, 3395945, 98793, 338945, 98499, 8484945, 58899, 839555, 8789, 38555, 8779, 85955, 387979, 8595555, 399899, 8347945, 47793, 949595, 5853, 578735, 7755853, 587935, 7387853, 45745, 8743, 38745, 9753, 34835, 9754553, 44835, 8553, 45345, 738533, 5345, 73593, 473895, 75543, 4478845, 995533, 345, 98393,...

The largest term is a(659)=9474344395

/Lars B

-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Eric Angelini
Skickat: den 21 december 2015 14:34
Till: Sequence Fanatics <seqfan at list.seqfan.eu>
Kopia: alexandre.wajnberg at skynet.be
Ämne: [seqfan] Forbidden digits =2016

Hello SeqFans,

here is an attempt to build a seq were :
-- a(n) and a(n+1) do not contain 2, 0, 1 or 6
-- the sum a(n)+a(n+1) does not contain 2, 0, 1 or 6
-- the product a(n)*a(n+1) does not contain 2, 0, 1 or 6

   S  =  5,    79,    455,   7439, ...
Sum:        84    534    7894
Prod:      395   35945  3384745

I don't know if this is the lexicographically first such seq -- but it seems to work...

Best wishes for the next year to you all -- and many thanks to the Seqfans who have helped, corrected and published some of my silly ideas of 2015!

É.


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