A336658 Numbers k such that k and k+1 both have the prime signature (2,1,1,1) (A189982).

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

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