A137982 Closest pair of primes p <= q such that p + q = n! Sequence gives the lesser member p of the pair.

3, 11, 59, 353, 2447, 20147, 181421, 1814347, 19958353, 239500727, 3113510341, 43589145527, 653837183849, 10461394943537, 177843714047843, 3201186852863803, 60822550204415273, 1216451004088319887, 25545471085854719707, 562000363888803839453, 12926008369442488319633

Offset

3,1

Links

Andrew Howroyd, Table of n, a(n) for n = 3..100

Formula

a(n) = A112823(n!/2). - Andrew Howroyd, Feb 02 2020

Example

3! = 3 + 3,
4! = 11 + 13,
5! = 59 + 61,
6! = 353 + 367.
p = 3,11,59,353,2447,20147,181421,1814347,19958353,239500727,3113510341,43589145527,653837183849;
q = 3,13,61,367,2593,20173,181459,1814453,19958447,239500873,3113510459,43589145673,653837184151;
q-p = 0,2,2,14,146,26,38,106,94,146,118,146,302.

Prog

(PARI) \\ here b(n) is A112823.
b(n)={my(p=precprime(n)); while(p && !isprime(2*n-p), p = precprime(p-1)); p}
a(n)={b(n!/2)} \\ Andrew Howroyd, Feb 02 2020

Crossrefs

Cf. A112823.

Sequence in context: A290484 A156560 A028342 * A193364 A074509 A343623

Adjacent sequences: A137979 A137980 A137981 * A137983 A137984 A137985

Keyword

nonn

Author

Zak Seidov, Apr 29 2008

Extensions

Terms a(16) and beyond from Andrew Howroyd, Feb 02 2020

Status

approved