A195468 - OEIS

%I #39 Nov 09 2023 08:52:57

%S 85487,104651,253241,280601,458987,580337,1082399,1207361,1251947,

%T 1678541,2811269,3090089,5044031,5173601,5590619,9567671,10323767,

%U 12263129,16324001,18073817,20647619,21303341,22849481,25080101,28527047,33627299,36307979,43363601,45414431

%N Lesser of overpseudo-twin-primes to base 2 defined in Comment.

%C If h_2(n) is the multiplicative order of 2 modulo n, r_2(n) is the number of cyclotomic cosets of 2 modulo n then, by the definition, n is an overpseudoprime to base 2 if h_2(n)*r_2(n)+1=n. These numbers are in A141232.

%C We call numbers {n,n+2} overpseudo-twin-primes to base 2 if each of them either prime or overpseudoprime to base 2, but no two are primes.

%H Amiram Eldar, <a href="/A195468/b195468.txt">Table of n, a(n) for n = 1..20863</a> (terms below 10^15)

%H Vladimir Shevelev, <a href="http://arxiv.org/abs/0806.3412">Overpseudoprimes, Mersenne Numbers and Wieferich primes</a> arXiv:0806.3412 [math.NT], 2008-2012.

%H Vladimir Shevelev, <a href="http://arxiv.org/abs/0807.2332">Process of "primoverization" of numbers of the form a^n-1</a>, arxiv:0807.2332 [math.NT], 2008.

%Y Cf. A141232, A002326, A006694, A137576, A001567, A002997, A194231, A192297.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Oct 12 2011

%E More terms from _Amiram Eldar_, Sep 21 2019