A379743 a(n) is the smallest prime whose digital sum in base n is n.

3, 5, 7, 13, 11, 13, 29, 17, 19, 31, 23, 37, 53, 29, 31, 97, 103, 37, 191, 41, 43, 67, 47, 73, 101, 53, 109, 113, 59, 61, 311, 97, 67, 103, 71, 73, 149, 191, 79, 241, 83, 127, 173, 89, 181, 139, 283, 97, 197, 101, 103, 157, 107, 109, 331, 113, 229, 233, 709, 181, 367, 311, 127, 193, 131, 199, 269

Offset: 2

Author

Robert Israel, Dec 31 2024

Keywords

• nonn
• base
• look

Comments

For n <= 10^5, a(n) < n^2, thus a(n) = k*n + (n-k) for some k, 1 <= k < n. Is this true for all n?

Examples

			a(5) = 13 because the prime 13 = 23_5 with 2 + 3 = 5, and no smaller prime works.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A214123.

Programs

Maple

f:= proc(n) local k,v,x;
  for k from 1 do
    v:= convert(convert(k,base,n),`+`);
    if v > n then next fi;
    x:= n*k+(n-v);
    if isprime(x) then return x fi
 od
end proc:
map(f, [$2..100]);

Mathematica

a[n_]:=Module[{k=1}, While[DigitSum[Prime[k],n]!=n, k++]; Prime[k]]; Array[a,67,2] (* Stefano Spezia, Jan 04 2025 *)