cp's OEIS Frontend

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

%I A261078 #16 Feb 22 2025 20:05:50
%S A261078 6,15,21,33,35,57,65,77,143,161,185,201,209,221,323,377,393,437,473,
%T A261078 497,713,899,1073,1457,1517,1529,1577,1763,1769,1841,1961,2021,2537,
%U A261078 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
%N A261078 Semiprimes p*q such that q = p + 2^k for some k >= 0.
%C A261078 Terms ending with digit 5 (in decimal) are very rare, because terms of A123250 are rare.
%H A261078 Antti Karttunen, <a href="/A261078/b261078.txt">Table of n, a(n) for n = 1..10000</a>
%e A261078 6 = 2*3 is present as 3 = 2 + 2^0.
%e A261078 15 = 3*5 is present as 5 = 3 + 2^1.
%e A261078 35 = 5*7 is present as 7 = 5 + 2^1.
%o A261078 (PARI)
%o A261078 A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
%o A261078 isA261078(n) = { my(d); if(bigomega(n)!=2, return(0), d = (n/A020639(n)) - A020639(n); (d && !bitand(d,d-1))); };
%o A261078 i=0; n=0; while(i < 10000, n++; if(isA261078(n), i++; write("b261078.txt", i, " ", n)));
%o A261078 (Scheme)
%o A261078 ;; With _Antti Karttunen_'s IntSeq-library.
%o A261078 (define A261078 (MATCHING-POS 1 1 (lambda (n) (and (= 2 (A001222 n)) (pow2? (- (A006530 n) (A020639 n)))))))
%o A261078 (define (pow2? n) (and (> n 0) (zero? (A004198bi n (- n 1))))) ;; A004198bi implements bitwise-AND (Cf. A004198)
%Y A261078 Cf. A001222, A004198, A006530, A020639, A123250.
%Y A261078 Cf. also A261073, A261077 (subsequences).
%K A261078 nonn
%O A261078 1,1
%A A261078 _Antti Karttunen_, Sep 22 2015