cp's OEIS Frontend

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.

%I A245358 #18 Dec 10 2015 09:29:09
%S A245358 2,12,199,113,14459,223,1133779,1111222,2225,222222666689,
%T A245358 111111111222344678,112225556779999,1122233333333444555888888,
%U A245358 111111111133333333334444555666
%N 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.
%C A245358 a(10) > 10^9.
%C A245358 a(n) will always be a number with nondecreasing digits.
%C A245358 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
%e A245358 1^1 + 1^1 + 3^1 = 5 is prime.
%e A245358 1^2 + 1^2 + 3^2 = 11 is prime.
%e A245358 1^3 + 1^3 + 3^3 = 29 is prime.
%e A245358 1^4 + 1^4 + 3^4 = 83 is prime.
%e A245358 Since 113 is the smallest number that does this for exponents 1, 2, 3, and 4, a(4) = 113.
%o A245358 (PARI)
%o A245358 a(n) = for(k=1,10^3,d=digits(n);if(!ispseudoprime(sum(i=1,#d,d[i]^k)),return(k-1)))
%o A245358 b(m) = for(n=1,10^9,if(a(n)==m,return(n)));return(0)
%o A245358 m=1;while(m<100,print1(b(m),", ");m++)
%K A245358 nonn,base,more
%O A245358 1,1
%A A245358 _Derek Orr_, Jul 18 2014
%E A245358 a(10)-a(14) added and definition corrected by _Chai Wah Wu_, Dec 07 2015