|
%I #37 Jul 23 2015 00:55:50
%S 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,
%T 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,
%U 0,0,0,0,0,3,2,1,0,0,1,0,0,0,0,0,0,0
%N Number of subsequent numbers, starting with n, for which A258881(x) = x + (sum of squares of digits of x) is prime.
%C This sequence is motivated by sequence A259391 and the "Prime puzzle 776".
%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_776.htm">Puzzle 776. Ten consecutive integers such that...</a>, PrimePuzzles.net, March 2015.
%F If a(n) > 0, then a(n+1) = a(n)-1.
%F a(n) > 0 iff n is in A076161.
%e For n = 0, A258881(0) = 0 is not prime.
%e For n = 1, A258881(1) = 1+1 = 2 is prime, but A258881(2) = 2+4 is not prime, therefore a(1)=1.
%e 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.
%e The next value of 10 occurs at index n = 1761702690, see A259391.
%o (PARI) a(n)=for(m=n,n+9e9,isprime(A258881(m))||return(m-n))
%Y Cf. A259391, A258881, A003132, A076161, A033936.
%K nonn,base
%O 0,11
%A _M. F. Hasler_, Jul 19 2015
|
