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%I #14 Jul 30 2020 02:14:01
%S 11780,20349,24794,33579,36764,37323,38324,38675,38709,42020,44505,
%T 47564,47684,51204,52155,53955,55419,56259,64844,68475,71379,71994,
%U 75284,77714,79134,80475,81548,81549,83420,85491,86715,87164,87380,90524,92364,94940,95403,95589
%N Numbers k such that k and k+1 both have the prime signature (2,1,1,1) (A189982).
%C Goldston et al. (2011) proved that this sequence is infinite.
%C Some consecutive terms are (81548, 81549), (141218, 141219), (179828, 179829). - _David A. Corneth_, Jul 29 2020
%H Amiram Eldar, <a href="/A336658/b336658.txt">Table of n, a(n) for n = 1..10000</a>
%H Daniel A. Goldston, Sidney W. Graham, Janos Pintz, and Cem Y. Yıldırım, <a href="https://doi.org/10.1093/imrn/rnq124">Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers</a>, International Mathematics Research Notices, Vol. 2011, No. 7 (2011), pp. 1439-1450, <a href="https://arxiv.org/abs/0803.2636">preprint</a>, arXiv:0803.2636 [math.NT], 2006.
%e 11780 is a term since 11780 = 2^2 * 5 * 19 * 31 and 11781 = 3^2 * 7 * 11 * 17.
%t seqQ[n_] := Sort[FactorInteger[n][[;; , 2]]] == {1, 1, 1, 2}; Select[Range[10^5], seqQ[#] && seqQ[# + 1] &]
%Y Subsequence of A140078 and A274362.
%Y Cf. A189982.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jul 28 2020