A051861 Twice the positions in A051686 at which new primes appear in that sequence.

2, 4, 16, 38, 58, 72, 148, 170, 178, 282, 388, 446, 512, 652, 656, 758, 836, 856, 1514, 1592, 1648, 1712, 1906, 1918, 2034, 2606, 2758, 4094, 4936, 5624, 5758, 5842, 5924, 6764, 8188, 10570, 10922, 11072, 11482, 13082, 13972, 14626, 15212, 16018, 18986

Offset: 1

Author

Labos Elemer, Dec 14 1999

Keywords

• nonn

Comments

Halving this sequence gives 1, 2, 8, 19, ..., 256, 326, ..., 47764, ..., the indices in A051686 at which primes appear which have not appeared before.

This sequence lists the terms of A051692 in ascending order, whereas A051692 lists them in increasing order of the emerging primes in A051686.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..400

Crossrefs

Cf. A051686, A051692, A005384.

Programs

Mathematica

s[n_] := Module[{p = 2}, While[! PrimeQ[2*n*p + 1], p = NextPrime[p]]; p]; seq[len_] := Module[{t = {}, v = {}, n = 1, c = 0, p}, While[c < len, p = s[n]; If[FreeQ[t, p], c++; AppendTo[t, p]; AppendTo[v, 2*n]]; n++]; v]; seq[45] (* Amiram Eldar, Feb 28 2025 *)

PARI

s(n) = {my(p = 2); while(!isprime(2*n*p + 1), p = nextprime(p+1)); p;}
isin(list, k) = {for(i = 1, #list, if(list[i] == k, return(1))); 0};
list(len) = {my(t = List(), n = 1, c = 0, p); while(c < len, p = s(n); if(!isin(t, p), c++; listput(t, p); print1(2*n, ", ")); n++);} \\ Amiram Eldar, Feb 28 2025

Extensions

Edited by Jon E. Schoenfield, May 28 2018