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

1,1

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.

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A115250 A018304 A289988 * A053745 A019275 A396475

Adjacent sequences: A051689 A051690 A051691 * A051693 A051694 A051695

Keyword

nonn

Author

Labos Elemer

Extensions

More terms from Michel Marcus, Jun 08 2018

Status

approved