|
|
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
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|