A263990 Nonsquare numbers k such that k and k+1 are semiprimes.

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

Offset: 1

Author

Zak Seidov, Oct 31 2015

Keywords

• nonn

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

Crossrefs

Subsequence of A070552, A086263.

Cf. A006881, A039833, A109288, A263951.

Programs

Mathematica

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

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

Formula

a(n) = A109288(n) - 1. - Amiram Eldar, Aug 08 2025