A051692 a(n) is twice the smallest k such that A051686(k) = prime(n).

2, 4, 38, 16, 170, 72, 446, 58, 512, 282, 178, 148, 758, 856, 836, 1592, 1712, 388, 1906, 2606, 2034, 1918, 656, 5924, 1648, 13082, 652, 1514, 2758, 10922, 5758, 18986, 6764, 10570, 20918, 4936, 8188, 5842, 4094, 30710, 15212, 11482, 57932, 14626, 5624, 36232, 16018, 57874

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

The sequence is based on the first 50000 terms of A051686, in which the first 54 primes (2,3,...,251) appear along with 19 others, the largest of which is A051686(37976) = 823.

Examples

			The 25th term in this sequence is 1648. This means that prime(25) = 97 arises in A051686 as A051686(1648/2) = A051686(824). Thus, 1648 is the first term in the sequence {..., 2k, ...} = {1648, 1798, 4108, ...} with the property that 2k*97 + 1 = 194k + 1 is also a prime, moreover the smallest one: 159857.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..376

Crossrefs

Cf. A005384, A051644-A051654, A051860, A051861.

Programs

Mathematica

s[n_] := Module[{p = 2, i = 1}, While[! PrimeQ[2*n*p + 1], p = NextPrime[p]; i++]; i]; seq[len_] := Module[{v = Table[0, {len}], c = 0, k = 1, i}, While[c < len, i = s[k]; If[i <= len && v[[i]] == 0, v[[i]] = 2*k; c++]; k++]; v]; seq[48] (* Amiram Eldar, Feb 28 2025 *)

PARI

a051686(n) = my(p=2); while(!isprime(2*n*p+1), p = nextprime(p+1)); p;
a(n) = my(k=1); while(a051686(k) != prime(n), k++); 2*k; \\ Michel Marcus, Jun 08 2018

PARI

s(n) = {my(p = 2, i = 1); while(!isprime(2*n*p + 1), p = nextprime(p+1); i++); i;}
list(len) = {my(v = vector(len), c = 0, k = 1, i); while(c < len, i = s(k); if(i <= len && v[i] == 0, v[i] = 2*k; c++); k++); v;} \\ Amiram Eldar, Feb 28 2025

Extensions

More terms from Michel Marcus, Jun 08 2018