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

Author

Zak Seidov, Apr 29 2008

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A112823.

Programs

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

Formula

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

Extensions

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