A071602 -id:A071602 - cp's OEIS frontend

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

Robert Israel, Feb 17 2025

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

			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.

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

Cf. A071602.

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);

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 *)

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

A381245 Numbers that are partial sums of the reverses of the sequence of primes and are reverses of primes.

Original entry on oeis.org

2, 5, 17, 358, 775, 3145, 7813, 10277, 13978, 15232, 19478, 32324, 36056, 70042, 71396, 72893, 76856, 102374, 141982, 155585, 301291, 331357, 332588, 354643, 717817, 763586, 791641, 799532, 922981, 931705, 935117, 940241, 952975, 993551, 1020461, 1028383, 1060075, 1094099, 1126831, 1145257

Offset: 1

Robert Israel, Feb 17 2025

Intersection of A071602 (in that order) and A004087.

			a(4) = 358 is a term because 358 = A071602(11) is the sum of the reverses of the first 11 primes, and is the reverse of the prime 853.
A071602(7) = 130 is not a term, because 130 is not the reverse of a prime, even though the reverse of 130 is a prime.

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

Cf. A004087, A071602.

rev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
PR:= map(rev, select(isprime, [$1..10000]):
SPR:= ListTools:-PartialSums(PR):
select(t -> t mod 10 <> 0 and isprime(rev(t)),SPR);

cp's OEIS Frontend

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

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