A381868 Starting from the n-th prime, a(n) is the minimum number > 1 of consecutive primes whose sum is the greater of a twin prime pair.

2, 137, 95, 3, 339, 93, 51, 5, 49, 5, 3, 115, 91, 35, 331, 7, 11, 3, 19, 29, 5, 187, 515, 15, 13, 79, 203, 11, 3, 69, 9, 93, 7, 13, 13, 5, 189, 71, 289, 419, 35, 239, 11, 9, 9, 33, 3, 129, 57, 75, 71, 53, 23, 121, 523, 13, 11, 3, 9, 11, 3, 193, 87, 5, 23, 181, 115, 3

Offset

1,1

Links

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

Example

a(4) = 3 because we need to add the primes 7, 11 and 13, to reach the greater of the twin prime pair (29 and 31).

Maple

f:= proc(p) local t, q, i;
  t:= p; q:= p;
  for i from 2 do
    q:= nextprime(q);
    t:= t+q;
    if isprime(t) and isprime(t-2) then return i fi
  od
end proc:
seq(f(ithprime(i)), i=1..100); # Robert Israel, May 08 2025

Prog

(Python)
import sympy
def a(n):
   p=sympy.prime(n); s=p; c=1
   p=sympy.nextprime(p); s+=p; c+=1
   while not(sympy.isprime(s-2) and sympy.isprime(s)):p=sympy.nextprime(p); s+=p; c+=1
   return c
(PARI) a(n) = my(p=prime(n), s=p, nb=1); while (!isprime(s-2) || !isprime(s) || (nb==1), p=nextprime(p+1); s+=p; nb++); nb; \\ Michel Marcus, Apr 02 2025

Crossrefs

Cf. A006512, A381855, A381766.

Sequence in context: A216030 A216083 A000662 * A139907 A195379 A221227

Adjacent sequences: A381865 A381866 A381867 * A381869 A381870 A381871

Keyword

nonn

Author

Abhiram R Devesh, Mar 08 2025

Status

approved