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A307217 Semiprimes p*q such that 2^(p+q) == 1 (mod p*q). 0

%I #38 Apr 11 2019 22:36:25

%S 9,15,35,119,5543,74447,90859,110767,222179,389993,1526849,2927297,

%T 3626699,4559939,24017531,137051711,160832099,229731743,627699239,

%U 880021141,1001124539,1041287603,1104903617,1592658611,1717999139,8843679683,15575602979,15614760199,20374337479

%N Semiprimes p*q such that 2^(p+q) == 1 (mod p*q).

%C For k > 9, these are semiprimes k such that 2^(k+1) == 1 (mod k): semiprimes in A187787.

%C In this sequence, only 9 is a perfect square. - _Jinyuan Wang_, Mar 30 2019

%o (PARI) isok(k) = (bigomega(k)==2) && (Mod(2, k)^(k+1) == 1); \\ (for k > 9) _Michel Marcus_, Mar 29 2019

%o (Perl) use ntheory ":all"; forsemiprimes { print "$_\n" if powmod(2, vecsum(factor($_)), $_) == 1 } 4, 1e7; # _Daniel Suteu_, Mar 30 2019

%Y Cf. A001358, A046315, A127104, A187787, A208728.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Mar 29 2019

%E a(7)-a(18) from _Amiram Eldar_, Mar 29 2019

%E a(19)-a(29) from _Daniel Suteu_, Mar 29 2019

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Last modified April 16 05:35 EDT 2024. Contains 371697 sequences. (Running on oeis4.)