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Numbers k such that 4*k-1 is divisible only by primes of form 4*m-1 (i.e., by the Gaussian primes A002145).
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%I #14 Apr 01 2021 09:42:35

%S 1,2,3,5,6,7,8,11,12,15,16,17,18,20,21,25,26,27,32,33,35,37,38,41,42,

%T 43,45,48,50,52,53,56,57,58,60,61,63,66,68,70,71,77,78,83,86,87,90,91,

%U 92,95,96,97,100,105,106,108,110,111,116,117,120,121,122,123,125,126,131

%N Numbers k such that 4*k-1 is divisible only by primes of form 4*m-1 (i.e., by the Gaussian primes A002145).

%H Amiram Eldar, <a href="/A094180/b094180.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (A094179(n) + 1)/4. - _Amiram Eldar_, Apr 01 2021

%t Select[Range[150], AllTrue[FactorInteger[4*# - 1][[;; , 1]], Mod[#1, 4] == 3 &] &] (* _Amiram Eldar_, Apr 01 2021 *)

%o (PARI) {for(n=1,140,fac=factor(4*n-1);v=vector(matsize(fac)[1],j,fac[j,1])%4;if(vecmin(v)==3,print1(n,",")))} \\ _Klaus Brockhaus_, May 08 2004

%Y For the actual numbers 4*k-1, see A094179.

%Y Cf. A002145.

%K nonn

%O 1,2

%A _Lekraj Beedassy_, May 06 2004

%E More terms from _Klaus Brockhaus_, May 08 2004