[seqfan] sequences derived from A000255

Arie Bos(gmail) arie.0.bos at gmail.com
Mon Apr 8 12:42:40 CEST 2013


I stumbled the other day on A000975, A077854 and A153234, for which I noticed that a(n)+a(n+1)=2^(n+1)-1=A000225;
a(n)+a(n+2)=2^(n+2)-1 and a(n)+a(n+3)=2^n-1.

(If in A153234 the first three 0's were omitted, the last formula would have been a(n)+a(n+3)= 2^(n+3)-1.)

 

It is easy to continue this sequence of sequences with a(n)+a(n+k)=A000225(n+k), giving new entries (AFAICS) in OEIS for k=4,...,10:

0 1 3 7 15 30 60 120 240 481 963 1927 3855 7710 15420 30840 61680 123361 246723 493447 986895 1973790 3947580 7895160 15790320
31580641 63161283 126322567 252645135 505290270 1010580540 .

0 1 3 7 15 31 62 124 248 496 992 1985 3971 7943 15887 31775 63550 127100 254200 508400 1016800 2033601 4067203 8134407 16268815
32537631 65075262 130150524 260301048 520602096 1041204192 .

0 1 3 7 15 31 63 126 252 504 1008 2016 4032 8065 16131 32263 64527 129055 258111 516222 1032444 2064888 4129776 8259552 16519104
33038209 66076419 132152839 264305679 528611359 1057222719 .

0 1 3 7 15 31 63 127 254 508 1016 2032 4064 8128 16256 32513 65027 130055 260111 520223 1040447 2080895 4161790 8323580 16647160
33294320 66588640 133177280 266354560 532709121 1065418243 .

0 1 3 7 15 31 63 127 255 510 1020 2040 4080 8160 16320 32640 65280 130561 261123 522247 1044495 2088991 4177983 8355967 16711935
33423870 66847740 133695480 267390960 534781920 1069563840 .

0 1 3 7 15 31 63 127 255 511 1022 2044 4088 8176 16352 32704 65408 130816 261632 523265 1046531 2093063 4186127 8372255 16744511
33489023 66978047 133956095 267912190 535824380 1071648760 .

0 1 3 7 15 31 63 127 255 511 1023 2046 4092 8184 16368 32736 65472 130944 261888 523776 1047552 2095105 4190211 8380423 16760847
33521695 67043391 134086783 268173567 536347135 1072694271 .

 

But is this worthwhile to include these sequences in OEIS? 

Since this process is possible for any sequence.

 

Arie Bos



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