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%I #19 Sep 08 2022 08:46:16
%S 4,7,32,64
%N Prime powers k such that 3k + 4 is a perfect square.
%C This sequence is complete. For proof see the link. - _Altug Alkan_, Apr 15 2016
%H Altug Alkan, <a href="/A271676/a271676.txt">Proof of Fini and Full</a>
%e 4 is in this sequence because 3*4 + 4 = 16 = 4^2,
%e 7 is in this sequence because 3*7 + 4 = 25 = 5^2,
%e 32 is in this sequence because 3*32 + 4 = 100 = 10^2,
%e 64 is in this sequence because 3*64 + 4 = 196 = 14^2.
%t Select[Range[10^4], PrimePowerQ@ # && IntegerQ@ Sqrt[3 # + 4] &] (* _Michael De Vlieger_, Apr 12 2016 *)
%o (Magma) [n: n in [2..10000000] | IsPrimePower(n) and IsSquare(3*n + 4)];
%o (PARI) lista(nn) = for(n=1, nn, if(isprimepower(n) && issquare(3*n+4), print1(n, ", "))); \\ _Altug Alkan_, Apr 12 2016
%Y Cf. A000961, A271675.
%K nonn,fini,full
%O 1,1
%A _Juri-Stepan Gerasimov_, Apr 12 2016
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