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

%I A137982 #5 Feb 02 2020 19:51:04
%S A137982 3,11,59,353,2447,20147,181421,1814347,19958353,239500727,3113510341,
%T A137982 43589145527,653837183849,10461394943537,177843714047843,
%U A137982 3201186852863803,60822550204415273,1216451004088319887,25545471085854719707,562000363888803839453,12926008369442488319633
%N A137982 Closest pair of primes p <= q such that p + q = n! Sequence gives the lesser member p of the pair.
%H A137982 Andrew Howroyd, <a href="/A137982/b137982.txt">Table of n, a(n) for n = 3..100</a>
%F A137982 a(n) = A112823(n!/2). - _Andrew Howroyd_, Feb 02 2020
%e A137982 3! = 3 + 3,
%e A137982 4! = 11 + 13,
%e A137982 5! = 59 + 61,
%e A137982 6! = 353 + 367.
%e A137982 p = 3,11,59,353,2447,20147,181421,1814347,19958353,239500727,3113510341,43589145527,653837183849;
%e A137982 q = 3,13,61,367,2593,20173,181459,1814453,19958447,239500873,3113510459,43589145673,653837184151;
%e A137982 q-p = 0,2,2,14,146,26,38,106,94,146,118,146,302.
%o A137982 (PARI) \\ here b(n) is A112823.
%o A137982 b(n)={my(p=precprime(n)); while(p && !isprime(2*n-p), p = precprime(p-1)); p}
%o A137982 a(n)={b(n!/2)} \\ _Andrew Howroyd_, Feb 02 2020
%Y A137982 Cf. A112823.
%K A137982 nonn
%O A137982 3,1
%A A137982 _Zak Seidov_, Apr 29 2008
%E A137982 Terms a(16) and beyond from _Andrew Howroyd_, Feb 02 2020