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 A336658 Numbers k such that k and k+1 both have the prime signature (2,1,1,1) (A189982). 1
 11780, 20349, 24794, 33579, 36764, 37323, 38324, 38675, 38709, 42020, 44505, 47564, 47684, 51204, 52155, 53955, 55419, 56259, 64844, 68475, 71379, 71994, 75284, 77714, 79134, 80475, 81548, 81549, 83420, 85491, 86715, 87164, 87380, 90524, 92364, 94940, 95403, 95589 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Goldston et al. (2011) proved that this sequence is infinite. Some consecutive terms are (81548, 81549), (141218, 141219), (179828, 179829). - David A. Corneth, Jul 29 2020 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Daniel A. Goldston, Sidney W. Graham, Janos Pintz, and Cem Y. Yıldırım, Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers, International Mathematics Research Notices, Vol. 2011, No. 7 (2011), pp. 1439-1450, preprint, arXiv:0803.2636 [math.NT], 2006. EXAMPLE 11780 is a term since 11780 = 2^2 * 5 * 19 * 31 and 11781 = 3^2 * 7 * 11 * 17. MATHEMATICA seqQ[n_] := Sort[FactorInteger[n][[;; , 2]]] == {1, 1, 1, 2}; Select[Range[10^5], seqQ[#] && seqQ[# + 1] &] CROSSREFS Subsequence of A140078 and A274362. Cf. A189982. Sequence in context: A045307 A229411 A235316 * A321158 A046192 A210151 Adjacent sequences:  A336655 A336656 A336657 * A336659 A336660 A336661 KEYWORD nonn AUTHOR Amiram Eldar, Jul 28 2020 STATUS approved

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Last modified December 2 04:43 EST 2021. Contains 349437 sequences. (Running on oeis4.)