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A175942 Odd numbers n such that 4^n == 4 (mod 3*n) and 2^(n-1) == 4 (mod 3*(n-1)). 3
5, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 683, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2543, 2579, 2819, 2879 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, integers n == 5 (mod 6) such that 4^n == 4 (mod n) and 2^(n-1) == 4 (mod n-1).

Equivalently, integers n == 5 (mod 6) such that both n and (n-1)/2 are primes or (odd or even) Fermat 4-pseudoprimes (A122781).

Contains terms n of A175625 such that n == 5 (mod 6).

Contains terms n of A303448 such that n == 5 (mod 6).

Many composite terms of this sequence are of the form A007583(k)=(2^(2k+1) + 1)/3 (for k in A303009). It is unknown if there exist composite terms not of this form.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Range[1, 3001, 2], PowerMod[4, #, 3#]==4&&PowerMod[2, #-1, 3(#-1)]==4&] (* Harvey P. Dale, Aug 04 2018 *)

CROSSREFS

Sequence in context: A192954 A337437 A107010 * A181669 A306662 A052940

Adjacent sequences:  A175939 A175940 A175941 * A175943 A175944 A175945

KEYWORD

nonn

AUTHOR

Alzhekeyev Ascar M, Oct 27 2010

EXTENSIONS

Edited by Max Alekseyev, Apr 24 2018

STATUS

approved

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Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)