A175942 - OEIS

%I #38 Jun 25 2021 16:15:41

%S 5,11,23,47,59,83,107,167,179,227,263,347,359,383,467,479,503,563,587,

%T 683,719,839,863,887,983,1019,1187,1283,1307,1319,1367,1439,1487,1523,

%U 1619,1823,1907,2027,2039,2063,2099,2207,2447,2459,2543,2579,2819,2879

%N Odd numbers k such that 4^k == 4 (mod 3*k) and 2^(k-1) == 4 (mod 3*(k-1)).

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

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

%C Contains terms k of A175625 such that k == 5 (mod 6).

%C Contains terms k of A303448 such that k == 5 (mod 6).

%C 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.

%C 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

%H Harvey P. Dale, <a href="/A175942/b175942.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Range[1,3001,2],PowerMod[4,#,3#]==4&&PowerMod[2,#-1,3(#-1)]==4&] (* _Harvey P. Dale_, Aug 04 2018 *)

%Y Cf. A005385.

%K nonn

%O 1,1

%A _Alzhekeyev Ascar M_, Oct 27 2010

%E Edited by _Max Alekseyev_, Apr 24 2018