A130825 A list of pairs of consecutive primes identified by the first in the pair. A number can be found between these two primes that divides the sum of all primes up to this prime.

23, 31, 2741, 10613, 63199, 85853, 1039153, 2285291, 52962017, 66998857, 315796799, 336125837, 834972769, 1309750063, 1617454199, 2056836121, 5455816469, 9030058187, 10622144453, 237371071699, 341296396619

Offset

1,1

Comments

Both A045345 and A024011 are very restrictive in creating a sequence. The sequence herein presented has a bit more flexibility to produce qualifying divisors of the subtotal of the sum of all primes.

Links

Table of n, a(n) for n=1..21.

Formula

Move through the subtotals of all the primes, 2+3+5+7+11+..., until a composite between two consecutive primes divides the subtotal of all previous primes. If it does, then that prime immediately preceding the interval of composites is listed in the sequence.

Example

The subtotal for the primes up to 23 is 100. Between 23 and the next prime 29 there are the composites 24, 25, 26, 27 and 28 that are candidates for evenly dividing this subtotal of 100. We have 25 within this group and it does divide that subtotal of 100. Moving on to the subtotal up to 31, which is 160, we have the interval of composites 32, 33, 34, 35 and 36 as possible divisors of this current subtotal of 160. The number 32 divides this subtotal.

Crossrefs

Cf. A045345, A024011, A009560.

Sequence in context: A154291 A109559 A231401 * A087563 A093477 A070664

Adjacent sequences: A130822 A130823 A130824 * A130826 A130827 A130828

Keyword

uned,nonn

Author

J. M. Bergot, Aug 20 2007

Extensions

a(8)-a(21) from Donovan Johnson, Jul 11 2011

Status

approved