A212292 -id:A212292 - cp's OEIS frontend

A226484 Odd numbers not of the form p + q^2 + r^3 with p, q, and r prime.

1, 3, 5, 7, 9, 11, 13, 21, 27, 33, 37, 45, 51, 61, 127, 351

Offset: 1

Giovanni Resta, Jun 09 2013

There are no more terms < 10^11.

pp[n_] := Prime@ Range@ PrimePi@ n; upto[n_] := Complement[Range[1, n, 2],
  Flatten@Table[ q^2 + r^3 + pp[n - q^2 - r^3], {r, pp[n^(1/3)]}, {q, pp@Sqrt[n - r^3]}]]; upto[10^4]

A262436 Number of ways to represent 2n - 1 as p^2 + q^2 + r with p, q, and r prime, and p >= q.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 1, 2, 1, 1, 3, 0, 1, 3, 2, 2, 0, 2, 2, 2, 2, 2, 4, 2, 1, 4, 3, 3, 2, 3, 3, 1, 3, 4, 4, 5, 0, 2, 5, 2, 4, 3, 2, 4, 1, 4, 3, 5, 2, 3, 5, 1, 4, 6, 2, 5, 2, 2, 4, 3, 3, 3, 5, 3, 3, 5, 2, 4, 6, 3, 3, 4, 2, 6, 6, 3, 3, 5, 3, 3, 6, 3

Offset: 1

Peter Kagey, Sep 22 2015

nonn

k is in A212292 if and only if a((k+1)/2) = 0.

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A212292.

a(16) = 3 because there are three different ways to represent 16 * 2 - 1 = 31 in the form p^2 + q^2 + r with p, q, and r prime, and p >= q:
2^2 + 2^2 + 23,
3^3 + 3^3 + 13,
5^2 + 2^2 + 2.

cp's OEIS Frontend

A226484 Odd numbers not of the form p + q^2 + r^3 with p, q, and r prime.

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