A196874 Smallest prime(k) such that prime(k+n) - prime(k) is a perfect square.

2, 3, 43, 2, 7, 3, 61, 23, 17, 5, 109, 73, 67, 37, 19, 7, 3, 127, 73, 67, 31, 2, 277, 7, 3, 79, 89, 47, 53, 19, 13, 5, 151, 157, 1033, 73, 61, 31, 37, 307, 397, 1129, 163, 3, 103, 97, 613, 2, 587, 37, 13, 7, 197, 1009, 107, 137, 73, 613, 43, 23, 29, 13, 7, 193

Offset

1,1

Comments

The corresponding indices k are in A196815.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 43 is the smallest initial prime of a subset of 4 consecutive primes {43, 47, 53, 59} such that 59 - 43 = 16 = 4^2.

Maple

A196874:= proc(n)
for k from 1 do
if issqr(ithprime(k+n)-ithprime(k)) then
return ithprime(k);
end if;
end do:
end proc:
seq(A196874(n), n=1..80) ; # (see A196815) R. J. Mathar, Oct 06 2011

Mathematica

spk[n_]:=Module[{k=1}, While[!IntegerQ[Sqrt[Prime[n+k]-Prime[k]]], k++]; Prime[k]]; Array[spk, 70] (* Harvey P. Dale, Jul 23 2012 *)

Prog

(PARI) a(n) = {my(k=1); while (! issquare(prime(k+n)- prime(k)), k++); prime(k); } \\ Michel Marcus, Dec 28 2015

Crossrefs

Cf. A000040, A196815.

Sequence in context: A101821 A121475 A334533 * A087571 A126018 A257467

Adjacent sequences: A196871 A196872 A196873 * A196875 A196876 A196877

Keyword

nonn

Author

Michel Lagneau, Oct 07 2011

Status

approved