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A196874 Smallest prime(k) such that prime(k+n) - prime(k) is a perfect square. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 23 19:00 EDT 2021. Contains 346259 sequences. (Running on oeis4.)