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

%I A051861 #20 Feb 28 2025 05:56:58
%S A051861 2,4,16,38,58,72,148,170,178,282,388,446,512,652,656,758,836,856,1514,
%T A051861 1592,1648,1712,1906,1918,2034,2606,2758,4094,4936,5624,5758,5842,
%U A051861 5924,6764,8188,10570,10922,11072,11482,13082,13972,14626,15212,16018,18986
%N A051861 Twice the positions in A051686 at which new primes appear in that sequence.
%C A051861 Halving this sequence gives 1, 2, 8, 19, ..., 256, 326, ..., 47764, ..., the indices in A051686 at which primes appear which have not appeared before.
%C A051861 This sequence lists the terms of A051692 in ascending order, whereas A051692 lists them in increasing order of the emerging primes in A051686.
%H A051861 Amiram Eldar, <a href="/A051861/b051861.txt">Table of n, a(n) for n = 1..400</a>
%t A051861 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 *)
%o A051861 (PARI) s(n) = {my(p = 2); while(!isprime(2*n*p + 1), p = nextprime(p+1)); p;}
%o A051861 isin(list, k) = {for(i = 1, #list, if(list[i] == k, return(1))); 0};
%o A051861 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
%Y A051861 Cf. A051686, A051692, A005384.
%K A051861 nonn
%O A051861 1,1
%A A051861 _Labos Elemer_, Dec 14 1999
%E A051861 Edited by _Jon E. Schoenfield_, May 28 2018