

A128311


Remainder upon division of 2^(n1)1 by n.


2



0, 1, 0, 3, 0, 1, 0, 7, 3, 1, 0, 7, 0, 1, 3, 15, 0, 13, 0, 7, 3, 1, 0, 7, 15, 1, 12, 7, 0, 1, 0, 31, 3, 1, 8, 31, 0, 1, 3, 7, 0, 31, 0, 7, 30, 1, 0, 31, 14, 11, 3, 7, 0, 13, 48, 15, 3, 1, 0, 7, 0, 1, 3, 63, 15, 31, 0, 7, 3, 21, 0, 31, 0, 1, 33, 7, 8, 31, 0, 47, 39, 1, 0, 31, 15, 1, 3, 39, 0, 31, 63
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OFFSET

1,4


COMMENTS

By Fermat's little theorem, if p>2 is prime, then 2^(p1)=1 (mod p), thus a(p)=0. If a(n)=0, then n may be only pseudoprime, as for n = 341 = 11*31 [F. Sarrus, 1820].


LINKS

T. D. Noe, Table of n, a(n) for n=1..2048
Wikipedia, Fermat's little theorem


FORMULA

a(n) = M(n1)  n floor( M(n1)/n ) = M(n1)  max{ k in nZ  k <= M(n1) } where M(k)=2^k1.


EXAMPLE

a(1)=0 since any integer = 0 (mod 1)
a(2)=1 since 2^11=1 (mod 2),
a(3)=0 since 3 is a prime > 2,
a(4)=3 since 2^31=7=3 (mod 4)
a(341)=0 since 341=11*31 is a Sarrus number.


MATHEMATICA

Table[Mod[2^(n1)1, n], {n, 100}] (* Harvey P. Dale, Dec 22 2012 *)


PROG

(PARI) a(n)=(1<<(n1)1)%n


CROSSREFS

Cf. A001348 (Mersenne numbers), A001567 (Sarrus numbers: pseudoprimes to base 2), A002997 (Carmichael numbers), A084653, A001220 (Wieferich primes).
Sequence in context: A180049 A244454 A238123 * A132884 A319234 A210473
Adjacent sequences: A128308 A128309 A128310 * A128312 A128313 A128314


KEYWORD

nonn


AUTHOR

M. F. Hasler, May 04 2007


STATUS

approved



