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A195468 Lesser of overpseudo-twin-primes to base 2 defined in Comment. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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..619

V. Shevelev, Overpseudoprimes, Mersenne Numbers and Wieferich primes arXiv:0806.3412 [math.NT], 2008-2012.

V. 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.

Sequence in context: A031671 A010083 A235968 * A200657 A201269 A184212

Adjacent sequences:  A195465 A195466 A195467 * A195469 A195470 A195471

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Oct 12 2011

EXTENSIONS

More terms from Amiram Eldar, Sep 21 2019

STATUS

approved

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Last modified July 2 08:02 EDT 2020. Contains 335398 sequences. (Running on oeis4.)