A245359 Largest number k such that d_1^j + d_2^j + … + d_r^j is prime for all j = 1, 2, .. k, or 0 if no such k exists, where d_1, d_2, … d_r are the digits of n. a(n) = -1 if k is infinite.

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, -1, 2, 0, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 1, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 2

Offset: 1

Author

Derek Orr, Jul 18 2014

Keywords

• sign
• base

Comments

If a(n) = K and reorder the digits of n to make a new number, n'. Thus, a(n') = K.

Examples

			1^1 + 2^1 = 3 is prime.
1^2 + 2^2 = 5 is prime.
1^3 + 2^3 = 9 is not prime.
So a(12) and a(21) = 2.
		

Programs

PARI

a(n) = for(k=1,10^3,d=digits(n);if(!ispseudoprime(sum(i=1,#d,d[i]^k)),return(k-1)));return(-1)
n=1;while(n<100,print1(a(n),", "); n++)

Formula

a(A031974(n)) = -1 for all n.