A381217 a(n) is the least positive k such that the sum of the reverses of the first k primes is divisible by n.

1, 1, 10, 5, 2, 16, 5, 20, 20, 3, 9, 16, 7, 5, 10, 30, 4, 20, 68, 44, 16, 20, 9, 20, 19, 7, 26, 5, 47, 34, 19, 30, 20, 28, 99, 20, 29, 68, 54, 44, 86, 16, 41, 20, 74, 26, 40, 30, 16, 50, 28, 82, 97, 26, 101, 51, 68, 47, 6, 44, 38, 53, 42, 30, 7, 20, 38, 28, 10, 99, 110, 20, 72, 121, 103, 137, 189

Offset: 1

Author

Robert Israel, Feb 17 2025

Keywords

• nonn
• base

Comments

a(n) is the least k such that A071602(k) is divisible by n.

Examples

			a(3) = 10 because A071602(10) =  2 + 3 + 5 + 7 + 11 + 31 + 71 + 91 + 32 + 92 = 345 is divisible by 3, and no earlier term of A071602 is divisible by 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071602.

Programs

Maple

N:= 100: # for a(1) .. a(N)
rev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
V:= Vector(N):
Cands:= {$1..N}:
p:= 0: s:= 0:
for i from 1 while Cands <> {} do
  p:= nextprime(p); s:= s + rev(p);
S:= select(t -> s mod t = 0, Cands);
if S <> {} then
   V[convert(S,list)]:= i;
   Cands:= Cands minus S
fi
od:
convert(V,list);

Mathematica

s={};Do[ k=1;sm=0;Until[Divisible[sm,n],sm=sm+IntegerReverse[Prime[k]];k++];AppendTo[s,k-1],{n,77}];s (* James C. McMahon, Feb 19 2025 *)

PARI

sumkrp(k) = my(v=primes(k)); sum(i=1, k, fromdigits(Vecrev(digits(v[i])))); \\ A071602
a(n) = my(k=1); while(sumkrp(k) % n, k++); k; \\ Michel Marcus, Feb 17 2025