A255675 Least integer k such that the n-th prime of form m^2+1 divides the composite number k^2+1.

3, 3, 13, 31, 91, 183, 241, 381, 553, 651, 1261, 1561, 2863, 3081, 4291, 5403, 6973, 8011, 8743, 11991, 13341, 14281, 15253, 15751, 16771, 17823, 21171, 22351, 24181, 25441, 28731, 30801, 32221, 33673, 41413, 42231, 43891, 49953, 52671, 55461, 57361, 62251, 65281

Offset

1,1

Comments

a(n)= A002496(n)- A005574(n) for n>1 where A002496 are the primes of form m^2 + 1 and A005574 are the numbers m such that m^2 + 1 is prime.

Consequence: this is a subsequence of A002061 (central polygonal numbers of the form m^2 - m + 1).

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = A002496(n)- A005574(n) for n>1.

Example

a(3)=13 because A002496(3)=17, and 17 divides 13^2+1= 2*5*17.

Maple

with(numtheory):
nn:=1000:
for i from 1 to nn do:
   p:=i^2+1:
   if type(p, prime)=true
   then
  ii:=0:
   for k from i+1 to 10^6 while(ii=0) do:
   if irem(k^2+1, p)=0
   then
   ii:=1:printf(`%d, `, k):
     else
     fi:
   od:
   fi:
od:

Mathematica

Clear[m]; m[1]=1; m[2]=2; m[n_] := m[n] = For[j = m[n-1]+2, True, j = j+2, If[PrimeQ[j^2+1], Return[j]]]; a[n_] := For[k = m[n]+1, True, k++, If[ Divisible[k^2+1, m[n]^2+1], Return[k]]]; Array[a, 50] (* Jean-François Alcover, Jul 21 2015 *)

Crossrefs

Cf. A002061, A002496, A005574.

Sequence in context: A219314 A288146 A019154 * A272857 A092103 A233697

Adjacent sequences: A255672 A255673 A255674 * A255676 A255677 A255678

Keyword

nonn

Author

Michel Lagneau, Jul 10 2015

Status

approved