A248498 The smallest number of consecutive primes beginning with prime(n+1) added to prime(n) necessary to produce another prime.

1, 8, 2, 2, 2, 4, 2, 2, 2, 2, 2, 8, 2, 4, 6, 2, 4, 2, 2, 2, 4, 2, 2, 6, 6, 2, 6, 4, 2, 4, 4, 8, 4, 2, 2, 4, 2, 2, 10, 8, 4, 20, 4, 8, 2, 8, 2, 4, 54, 2, 6, 26, 8, 26, 6, 4, 4, 2, 8, 2, 2, 2, 4, 2, 6, 6, 10, 2, 2, 2, 4, 4, 6, 6, 2, 4, 2, 8, 2, 2, 4, 10, 2, 4, 46

Offset

1,2

Comments

Records are a(1) = 1, a(2) = 8, a(39) = 10, a(42) = 20, a(49) = 54, a(110) = 56, a(160) = 94, a(3070) = 158, a(13528) = 204, a(34721) = 216, a(391862) = 222, a(448696) = 298, a(651511) = 348, a(9776339) = 382, .... Assuming the sequence exists for all n it is unbounded so there are infinitely many records. - Charles R Greathouse IV, Oct 21 2014

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(1)=1 because 2+3=5 which is prime (only 1 prime added to 2 to get a prime).
a(2)=8 because 3+5+7+11+13+17+19+23+29=127 which is prime (8 consecutive primes added to 3), and all of the partial sums are composite.

Prog

(PARI) a(n) = my(p = prime(n), q = nextprime(p+1), s = p+q, nb = 1); while (! isprime(s), p=q; q=nextprime(p+1); s += q; nb++); nb; \\ Michel Marcus, Oct 07 2014

Crossrefs

Cf. A000040, A071196.

Sequence in context: A136711 A037920 A138997 * A133918 A072691 A021928

Adjacent sequences: A248495 A248496 A248497 * A248499 A248500 A248501

Keyword

nonn,easy

Author

Gil Broussard, Oct 07 2014

Status

approved