A261078 Semiprimes p*q such that q = p + 2^k for some k >= 0.

6, 15, 21, 33, 35, 57, 65, 77, 143, 161, 185, 201, 209, 221, 323, 377, 393, 437, 473, 497, 713, 899, 1073, 1457, 1517, 1529, 1577, 1763, 1769, 1841, 1961, 2021, 2537, 2993, 3233, 3473, 3497, 3599, 3713, 3737, 3953, 4553, 4601, 4757, 5183, 5561, 5609, 5753, 6497, 6557, 7217, 7313, 8633, 8777, 9593, 9797, 10001, 10265, 10403, 10841, 10961, 11009, 11021

Offset: 1

Author

Antti Karttunen, Sep 22 2015

Keywords

• nonn

Comments

Terms ending with digit 5 (in decimal) are very rare, because terms of A123250 are rare.

Examples

			6 = 2*3 is present as 3 = 2 + 2^0.
15 = 3*5 is present as 5 = 3 + 2^1.
35 = 5*7 is present as 7 = 5 + 2^1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A004198, A006530, A020639, A123250.

Cf. also A261073, A261077 (subsequences).

Programs

PARI

A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
isA261078(n) = { my(d); if(bigomega(n)!=2, return(0), d = (n/A020639(n)) - A020639(n); (d && !bitand(d,d-1))); };
i=0; n=0; while(i < 10000, n++; if(isA261078(n), i++; write("b261078.txt", i, " ", n)));

Scheme

;; With Antti Karttunen's IntSeq-library.
(define A261078 (MATCHING-POS 1 1 (lambda (n) (and (= 2 (A001222 n)) (pow2? (- (A006530 n) (A020639 n)))))))
(define (pow2? n) (and (> n 0) (zero? (A004198bi n (- n 1))))) ;; A004198bi implements bitwise-AND (Cf. A004198)