A219958 Integers n such that n^2 can be represented as 2p + 3q with p and q primes not necessarily distinct.

4, 5, 7, 8, 10, 11, 13, 15, 17, 19, 20, 22, 23, 25, 27, 28, 29, 31, 32, 35, 37, 38, 40, 41, 43, 45, 47, 49, 53, 55, 59, 61, 63, 65, 67, 68, 70, 71, 73, 75, 77, 79, 82, 83, 85, 87, 89, 91, 92, 95, 97, 98, 101, 103, 105, 107, 109, 110, 112, 113, 115, 117, 118

Offset

1,1

Links

Zak Seidov, Table of n, a(n) for n = 1..115

Example

4^2 = 16 = 2*5 + 3*2,
5^2 = 25 = 2*5 + 3*5,
7^2 = 49 = 2*5 + 3*13.
In case of multiple solutions (as for 5^2 and 7^2) just one solution (with least p) is shown.

Mathematica

mx = 50000; Select[Sqrt[Union[Reap[Do[p = Prime[k]; Do[ Sow[ 2 Prime[i] + 3 p], {i, PrimePi[(mx - 3 p)/2]}], {k, PrimePi[(mx - 4)/3]}]][[2, 1]]]], IntegerQ]; (*for first 115 terms *)
Take[Union[Select[Sqrt[2#[[1]]+3#[[2]]]&/@Tuples[Prime[ Range[1000]], 2], IntegerQ]], 70] (* Harvey P. Dale, Feb 08 2020 *)

Crossrefs

Cf. A079026, A219955, A219956, A219957.

Sequence in context: A231507 A097482 A191984 * A288753 A202186 A247467

Adjacent sequences: A219955 A219956 A219957 * A219959 A219960 A219961

Keyword

nonn

Author

Zak Seidov, Dec 02 2012

Status

approved