[seqfan] Re: a(n)+a(a(n)) is prime

Lars Blomberg lars.blomberg at visit.se
Sat Apr 11 19:36:31 CEST 2015


Hello,

I find
1, 3, 2, 5, 6, 7, 10, 9, 8, 13, 12, 11, 16, 15, 14, 21, 18, 19, 22, 23, 20, 25, 24, 29, 28, 27, 26, 31, 30, 37, 36, 33, 34, 39, 38, 35, 42, 41, 40, 43, 48, 47, 46, 45, 44, 51, 50, 49, 52, 53, 56, 55, 54, 59, 58, 57, 70, 69, 68, 61, 66, 63, 64, 67, 71, 73, 72, 81, 80, 79, 78, 77, 76, 75, 74, 87, 86, 85, 84, 83, 82, 91, 90, 89, 88, 93, 92, 103, 102, 101, 100, 99, 98, 95, 96, 97, 114, 113, 112, 111, 110, 109, 108, 105, 106, 117, 115, 119, 118, 123, 116, 121, 120, 125, 124, 135, 122, 133, 132, 131, 130, 129, 128, 127, 126, 137, 136, 141, 134, 139, 138, 145, 144, 143, 142, 147, 140, 155, 154, 153, 152, 151, 150, 149, 148, 156, 160, 159, 158, 157, 162, 161, 164, 163, 176, 175, 174, 173, 172, 171, 170, 169, 168, 167, 166, 165, 180, 179, 178, 177, 182, 181, 186, 185, 184, 183, 190, 189, 188, 187, 192, 191, 196, 195, 194, 193, 202, 201, 200, 199, 198, 197, 204, 203, 206, 205, 212, 211, 210, 209, 208, 207, 216, 215, 214, 213, 224, 223, 222, 221, 220, 219, 218, 217, 228, 227, 226, 225, 230, 229

S[22] seems to be 25 instead of 26. 

The first few unused values after 10,000 terms are
4, 17, 32, 60, 62, 65, 94, 104, 107, 146, 269, 272, 451, 574, 637, 672, 674, 676, 678, 683

Regards,
Lars

-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Eric Angelini
Skickat: den 11 april 2015 15:40
Till: Sequence Discussion list
Ämne: [seqfan] a(n)+a(a(n)) is prime


Hello SeqFans,
S is the lexicographically first seq where a(n)+a(a(n)) is prime.

[This is not http://oeis.org/A083569
as the integers 4, 17, etc. will never
appear here].

S=1,3,2,5,6,7,10,9,8,13,12,11,16,15,14,21,18,19,22,23,20,26,24,...

Example:
1 + (the 1st integer of S) is prime (1+1=2)
3 + (the 3rd integer of S) is prime (3+2=5)
2 + (the 2nd integer of S) is prime (2+3=5)
5 + (the 5th integer of S) is prime (5+6=11)
6 + (the 6th integer of S) is prime (6+7=13)
7 + (the 7th integer of S) is prime (7+10=17)
10 + (the 10th integer of S) is prime (10+13=23)
9 + (the 9th integer of S) is prime (9+8=17)
8 + (the 8th integer of S) is prime (8+9=17) etc.
S is always extended with the smallest
integer not yet in S and not leading
to a contradiction.

Best,
É.


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