

A263990


Nonsquare numbers k such that k and k+1 are semiprimes.


7



14, 21, 33, 34, 38, 57, 85, 86, 93, 94, 118, 122, 133, 141, 142, 145, 158, 177, 201, 202, 205, 213, 214, 217, 218, 253, 298, 301, 302, 326, 334, 381, 393, 394, 445, 446, 453, 481, 501, 514, 526, 537, 542, 553, 565, 622, 633, 634, 694, 697, 698, 706, 717, 745, 766, 778, 793, 802, 817, 842, 865, 878
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OFFSET

1,1


COMMENTS

If k and k+1 are semiprimes then k+1 is always nonsquare while k can be a square (see A263951). The sequence gives the nonsquare terms of A070552. Each of the numbers k and k+1 is a product of two distinct primes.
Numbers that are terms in A070552 but not in A263951.
The subsequence of triples of consecutive squarefree semiprimes is A039833.  R. J. Mathar, Aug 13 2019


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000


MATHEMATICA

Select[Range[1000], ! IntegerQ[Sqrt[#]] && 2 == PrimeOmega[#] == PrimeOmega[# + 1] &]


PROG

(PARI) is(n)=if(n%2, isprime((n+1)/2) && bigomega(n)==2 && !isprimepower(n), isprime(n/2) && bigomega(n+1)==2) \\ Charles R Greathouse IV, Apr 25 2016


CROSSREFS

Subsequence of A070552, A086263.
Cf. A006881, A263951.
Sequence in context: A120141 A240593 A121495 * A253810 A084995 A100466
Adjacent sequences: A263987 A263988 A263989 * A263991 A263992 A263993


KEYWORD

nonn


AUTHOR

Zak Seidov, Oct 31 2015


STATUS

approved



