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 A350118 Primes p for which the smallest m such that p*2^m + 1 is prime increases. Sequence terminates with the smallest prime Sierpiński number. 1
 2, 3, 7, 17, 19, 31, 47, 383, 2897, 3061, 5297, 7013, 10223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The smallest prime Sierpiński number is likely to be 271129. Related to A058887: this sequence is A058887 with repeated values removed. The following list shows that relation between these two sequences: a(2) = 3, A350119(2) = 1 => A058887(0..0) = 3; a(3) = 7, A350119(3) = 2 => A058887(1..1) = 7; a(4) = 17, A350119(4) = 3 => A058887(2..2) = 17; a(5) = 19, A350119(5) = 6 => A058887(3..5) = 19; a(6) = 31, A350119(6) = 8 => A058887(6..7) = 31; a(7) = 47, A350119(7) = 583 => A058887(8..582) = 47; a(8) = 383, A350119(8) = 6393 => A058887(583..6392) = 383; ... a(N) is the smallest prime Sierpiński number, A350119(N) = -1 => A058887(k) = a(N) for all k >= A350119(N-1). LINKS Table of n, a(n) for n=1..13. EXAMPLE Let b(p) be the smallest m such that p*2^m + 1 is prime. We have a(1) = 2 with b(2) = 0. The least prime p such that b(p) > 0 is p = 3 with b(3) = 1, so a(2) = 3. The least prime p such that b(p) > 1 is p = 7 with b(7) = 2, so a(3) = 7. The least prime p such that b(p) > 2 is p = 17 with b(17) = 3, so a(4) = 17. The least prime p such that b(p) > 3 is p = 19 with b(19) = 6, so a(5) = 19. The least prime p such that b(p) > 6 is p = 31 with b(31) = 8, so a(6) = 31. The least prime p such that b(p) > 8 is p = 47 with b(47) = 583, so a(7) = 47. PROG (PARI) b(p) = for(k=0, oo, if(isprime(p*2^k+1), return(k))) list(lim) = if(lim>=2, my(v=[2], r=0); forprime(p=2, lim, if(b(p)>r, r=b(p); v=concat(v, p))); v) CROSSREFS Cf. A058887, A057192, A350119, A064699, A076336 (Sierpiński numbers). Sequence in context: A174359 A160513 A154431 * A256917 A089144 A171430 Adjacent sequences: A350115 A350116 A350117 * A350119 A350120 A350121 KEYWORD nonn,fini,hard,more AUTHOR Jianing Song, Dec 14 2021 STATUS approved

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Last modified September 18 12:58 EDT 2024. Contains 376000 sequences. (Running on oeis4.)