A259567 Number of subsequent numbers, starting with n, for which A258881(x) = x + (sum of squares of digits of x) is prime.

0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

M. F. Hasler, Jul 19 2015

Keywords

• nonn
• base

Comments

This sequence is motivated by sequence A259391 and the "Prime puzzle 776".

Examples

			For n = 0, A258881(0) = 0 is not prime.
For n = 1, A258881(1) = 1+1 = 2 is prime, but A258881(2) = 2+4 is not prime, therefore a(1)=1.
For n = 10, A258881(10) = 10 + 1^2 + 0^2 = 11, A258881(11) = 11 + 1^2 + 1^2 = 13, A258881(12) = 12 + 1^2 + 2^2 = 17, ..., A258881(19) = 19 + 1^2 + 9^2 = 101 are all prime, but A258881(20) = 20 + 2^2 + 0^2 is not prime, therefore a(10) = 10.
The next value of 10 occurs at index n = 1761702690, see A259391.
		

Links

• C. Rivera, Puzzle 776. Ten consecutive integers such that..., PrimePuzzles.net, March 2015.

Crossrefs

Cf. A259391, A258881, A003132, A076161, A033936.

Programs

PARI

a(n)=for(m=n,n+9e9,isprime(A258881(m))||return(m-n))

Formula

If a(n) > 0, then a(n+1) = a(n)-1.

a(n) > 0 iff n is in A076161.