A071868 Number of integers k (1 <= k <= n) such that k^2+1 is prime.

1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16

Offset: 1

Author

Benoit Cloitre, Jun 09 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes, Acta Math., Vol. 44, No. 1 (1923), pp. 1-70. See Section 5.41.

Crossrefs

Cf. A002496, A005574, A199401.

Programs

Mathematica

Accumulate[Table[If[PrimeQ[k^2+1],1,0],{k,80}]] (* Harvey P. Dale, Jan 08 2020 *)

PARI

for(n=1,200,print1(sum(i=1,n,if(isprime(i^2+1)-1,0,1)),","))

Formula

Hardy and Littlewood conjectured that : a(n) ~ c* sqrt(n)/Log(n) where c = Product_{p prime} (1 - (-1)^((p-1)/2)/(p-1)) = 1.3728... (A199401).