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A175942
Odd numbers k such that 4^k == 4 (mod 3*k) and 2^(k-1) == 4 (mod 3*(k-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
OFFSET
1,1
COMMENTS
Equivalently, integers k == 5 (mod 6) such that 4^k == 4 (mod k) and 2^(k-1) == 4 (mod k-1).
Equivalently, integers k == 5 (mod 6) such that both k and (k-1)/2 are primes or (odd or even) Fermat 4-pseudoprimes (A122781).
Contains terms k of A175625 such that k == 5 (mod 6).
Contains terms k of A303448 such that k == 5 (mod 6).
Many composite terms of this sequence are of the form A007583(m) = (2^(2m+1) + 1)/3 (for m in A303009). It is unknown if there exist composite terms not of this form.
Numbers k such that 2^(k-1) == 3k+1 (mod 3(k-1)k). This sequence contains all safe primes except 7. The term a(20) = 683 = 2*341+1 is the smallest prime that is not safe. - Thomas Ordowski, Jun 07 2021
LINKS
MATHEMATICA
Select[Range[1, 3001, 2], PowerMod[4, #, 3#]==4&&PowerMod[2, #-1, 3(#-1)]==4&] (* Harvey P. Dale, Aug 04 2018 *)
CROSSREFS
Cf. A005385.
Sequence in context: A192954 A337437 A107010 * A181669 A362082 A306662
KEYWORD
nonn
AUTHOR
Alzhekeyev Ascar M, Oct 27 2010
EXTENSIONS
Edited by Max Alekseyev, Apr 24 2018
STATUS
approved