A381869 Smallest starting prime for which the sum of 2*n consecutive primes is 0 modulo 10, or -1 if no such prime exists.

13, 11, 7, 7, 13, 17, 7, 17, 37, 3, 7, 41, 7, 7, 11, 11, 11, 11, 11, 13, 11, 13, 11, 7, 7, 17, 7, 43, 41, 3, 3, 13, 11, 7, 13, 19, 7, 11, 11, 29, 7, 43, 3, 7, 11, 13, 23, 29, 3, 7, 7, 11, 11, 11, 19, 13, 5, 5, 13, 37, 17, 3, 3, 7, 17, 17, 3, 11, 19, 13, 3, 7, 23

Offset

1,1

Links

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

Example

a(1) = 13, because 13 and 17 are 2*1 = 2 consecutive primes such that 13 + 17 = 20 and 20 modulo 10 = 0, and no smaller prime has this property.

Maple

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):
S:= ListTools:-PartialSums(P):
f:= proc(n) local j, t;
  for j from 1 do
    if S[2*n+j] - S[j] mod 10 = 0 then return P[j+1] fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, May 08 2025

Mathematica

Do[i=1; Until[Mod[Total[Prime[Range[i, i+2*n-1]]], 10]==0, i++]; a[n]=Prime[i], {n, 73}]; Array[a, 73] (* James C. McMahon, Mar 23 2025 *)

Prog

(PARI) isok(p, n) = my(i=primepi(p), q=prime(2*n+i-1)); vecsum(apply(x->Mod(x, 10), primes([p, q]))) == 0;
a(n) = my(p=3); while (!isok(p, n), p=nextprime(p+1)); p; \\ Michel Marcus, Mar 09 2025
(Python)
from sympy import nextprime, prime, sieve
def a(n):
    plst = list(sieve.primerange(3, prime(2*n+1)+1))
    s = sum(plst)
    while s%10:
        q = nextprime(plst[-1])
        s += (q-plst[0])
        plst = plst[1:] + [q]
    return plst[0]
print([a(n) for n in range(1, 74)]) # Michael S. Branicky, Mar 09 2025

Crossrefs

Cf. A007652, A111324.

Sequence in context: A152298 A158956 A259663 * A392136 A160130 A340803

Adjacent sequences: A381866 A381867 A381868 * A381870 A381871 A381872

Keyword

nonn

Author

Jean-Marc Rebert, Mar 09 2025

Status

approved