A357190 a(n) is the least prime p such that A234575(p, A007953(p)) is the n-th power of a prime.

17, 13, 131, 107, 383, 613, 43607, 1021, 334403, 26099, 40637, 138967, 212867, 360049, 502210997, 2227399, 5682166613, 7339303, 13630913, 35650627, 92273957, 142605709, 4424729404133, 671087119, 42364430471219, 2684353351, 404156666702231, 10737417109, 4872756792902003

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 25 2022

Keywords

• nonn
• base

Comments

a(n) is the least prime p such that the sum of the quotient and remainder on division of p by the sum of digits of p is the n-th power of an integer.

Examples

			a(3) = 131 because 131 is prime, has sum of digits 5, 131 = 26*5 + 1 and 26 + 1 = 27 = 3^3 where 3 is prime; and 131 is the least prime that works.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A007953, A234575.

Programs

Maple

g:= proc(t,M) local s,q,r,n;
  for s from 2 to 9*M do
    for r from s-1 to 1 by -1 do
      q:= t-r;
      n:= q*s+r;
      if convert(convert(n,base,10),`+`) = s and isprime(n) then return n fi;
      if n >= 10^M then return -1 fi;
   od od;
   -1
end proc:
G:= proc(m) local i,M,found,v,r;
  found:= false; r:= infinity;
  for M from 3 while not found do
    for i from 1 while ithprime(i)^m < 10^M do
      v:= g(ithprime(i)^m, M);
      if v > 0 then found:= true; r:= min(v,r) fi
  od od:
  r
end proc:
map(G, [$1..30]);