A051861 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

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 *)

PROG

(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

CROSSREFS

Cf. A051686, A051692, A005384.

Sequence in context: A379525 A000216 A110998 * A296297 A290265 A223093

Adjacent sequences: A051858 A051859 A051860 * A051862 A051863 A051864

KEYWORD

nonn,changed

AUTHOR

Labos Elemer, Dec 14 1999

EXTENSIONS

Edited by Jon E. Schoenfield, May 28 2018

STATUS

approved