

A248498


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


1



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
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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



