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

1,1

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

Links

Table of n, a(n) for n=1..14.

Example

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.

Prog

(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++)

Crossrefs

Sequence in context: A110105 A182163 A367052 * A317350 A209832 A094157

Adjacent sequences: A245355 A245356 A245357 * A245359 A245360 A245361

Keyword

nonn,base,more

Author

Derek Orr, Jul 18 2014

Extensions

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

Status

approved