A245463 Smallest k such that A002522(k) and A002522(k+2n) are successive primes of the form m^2+1.

2, 6, 84, 66, 26, 134, 40, 94, 986, 184, 1524, 716, 864, 1246, 2986, 784, 350, 2174, 4796, 496, 7674, 13136, 3390, 12636, 5880, 9904, 16446, 37410, 6646, 10430, 56774, 31870, 9054, 24606, 12986, 54284, 35000, 124320, 114216, 58576, 88854, 85416, 18854, 3536

Offset

1,1

Comments

A002522(n) = n^2+1.

Subsequence of A005574.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..163

Example

a(3) = 84 because A002522(84)=7057 and A002522(84+2*3)= 8101 are two consecutive primes of the form m^2+1.

Maple

T:=array(1..44):
for n from 1 by 2 to 88 do:
   z:=0:ii:=0:
    for k from 2 to 10^7 while(z=0) do:
    p:=k^2+1:
    if type(p, prime)=false
     then
     ii:=ii+1:
     else
      if ii=n
      then
      printf ( "%d %d \n", (n+1)/2, k-n-1):T[(n+1)/2]:=k-n-1:z:=1:
      else
     fi:
     ii:=0:
    fi:
   od:
od:
print(T):

Prog

(PARI) for(n=1, 44, m=2; until(m==k+2*n, k=m; until(isprime(m^2+1), m++)); print1(k", ")) \\ Jens Kruse Andersen, Jul 22 2014

Crossrefs

Cf. A002496, A002522, A005574, A134406, A206400.

Sequence in context: A352284 A352313 A357028 * A325949 A055706 A376494

Adjacent sequences: A245460 A245461 A245462 * A245464 A245465 A245466

Keyword

nonn

Author

Michel Lagneau, Jul 22 2014

Status

approved