A245358 Least number m such that d_1^j + d_2^j + ... + d_k^j is prime for j = 1, 2, 3, ... n and is composite for j = n+1, where d_1, d_2, ... d_k are the digits of m.

2, 12, 199, 113, 14459, 223, 1133779, 1111222, 2225, 222222666689, 111111111222344678, 112225556779999, 1122233333333444555888888, 111111111133333333334444555666

Offset: 1

Author

Derek Orr, Jul 18 2014

Keywords

• nonn
• base
• more

Comments

a(10) > 10^9.

a(n) will always be a number with nondecreasing digits.

Except for 2, all terms have odd digit sum since the parity of d_1^j + d_2^j + ... + d_k^j does not change with j and the only numbers with nondecreasing digits and digit sum 2 are 2 and 11. - Chai Wah Wu, Dec 07 2015

Examples

			1^1 + 1^1 + 3^1 = 5 is prime.
1^2 + 1^2 + 3^2 = 11 is prime.
1^3 + 1^3 + 3^3 = 29 is prime.
1^4 + 1^4 + 3^4 = 83 is prime.
Since 113 is the smallest number that does this for exponents 1, 2, 3, and 4, a(4) = 113.
		

Programs

PARI

a(n) = for(k=1,10^3,d=digits(n);if(!ispseudoprime(sum(i=1,#d,d[i]^k)),return(k-1)))
b(m) = for(n=1,10^9,if(a(n)==m,return(n)));return(0)
m=1;while(m<100,print1(b(m),", ");m++)

Extensions

a(10)-a(14) added and definition corrected by Chai Wah Wu, Dec 07 2015