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

0,11

Comments

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

Links

Table of n, a(n) for n=0..85.

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

Formula

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

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

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A318255 A008956 A291560 * A022966 A023452 A052036

Adjacent sequences: A259564 A259565 A259566 * A259568 A259569 A259570

Keyword

nonn,base

Author

M. F. Hasler, Jul 19 2015

Status

approved