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

1,3

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A071602.

Sequence in context: A320938 A117256 A332837 * A050020 A050136 A053050

Adjacent sequences: A381214 A381215 A381216 * A381218 A381219 A381220

Keyword

nonn,base

Author

Robert Israel, Feb 17 2025

Status

approved