A195468 Lesser of overpseudo-twin-primes to base 2 defined in Comment.

85487, 104651, 253241, 280601, 458987, 580337, 1082399, 1207361, 1251947, 1678541, 2811269, 3090089, 5044031, 5173601, 5590619, 9567671, 10323767, 12263129, 16324001, 18073817, 20647619, 21303341, 22849481, 25080101, 28527047, 33627299, 36307979, 43363601, 45414431

Offset: 1

Author

Vladimir Shevelev, Oct 12 2011

Keywords

• nonn

Comments

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.

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..20863 (terms below 10^15)
• Vladimir Shevelev, Overpseudoprimes, Mersenne Numbers and Wieferich primes arXiv:0806.3412 [math.NT], 2008-2012.
• Vladimir Shevelev, Process of "primoverization" of numbers of the form a^n-1, arxiv:0807.2332 [math.NT], 2008.

Crossrefs

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

Extensions

More terms from Amiram Eldar, Sep 21 2019