A271676 Prime powers k such that 3k + 4 is a perfect square.

4, 7, 32, 64

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 12 2016

Keywords

• nonn
• fini
• full

Comments

This sequence is complete. For proof see the link. - Altug Alkan, Apr 15 2016

Examples

			4 is in this sequence because 3*4 + 4 = 16 = 4^2,
7 is in this sequence because 3*7 + 4 = 25 = 5^2,
32 is in this sequence because 3*32 + 4 = 100 = 10^2,
64 is in this sequence because 3*64 + 4 = 196 = 14^2.
		

Links

• Altug Alkan, Proof of Fini and Full

Crossrefs

Cf. A000961, A271675.

Programs

Magma

[n: n in [2..10000000] | IsPrimePower(n) and IsSquare(3*n + 4)];

Mathematica

Select[Range[10^4], PrimePowerQ@ # && IntegerQ@ Sqrt[3 # + 4] &] (* Michael De Vlieger, Apr 12 2016 *)

PARI

lista(nn) = for(n=1, nn, if(isprimepower(n) && issquare(3*n+4), print1(n, ", "))); \\ Altug Alkan, Apr 12 2016