A080693 Numbers of the form p^2*q + r*s where p,q,r,s are (not necessarily distinct) primes.

12, 14, 16, 17, 18, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86

Offset

1,1

Comments

A conjecture of Goldbach type says every number >= 26 is of this form.

Links

Table of n, a(n) for n=1..69.

Example

12=2^2*2 + 2*2

Maple

H := proc(n::posint) local p, q, r, s; p := 2; while p<=floor(sqrt((n-4)/2)) do q := 2; while q<=floor((n-4)/p^2) do s := 2; while s<=floor((n-p^2*q)/2) do r := (n-p^2*q)/s; if type(r, posint) then if isprime(r) then return(true, p, q, s, r); end if; end if; s := nextprime(s); end do; q := nextprime(q); end do; p := nextprime(p); end do; return(false); end:

Mathematica

Take[ Union[ Flatten[ Table[ Prime[p]^2*Prime[q] + Prime[r]*Prime[s], {p, 1, 6}, {q, 1, 15}, {r, 1, 15}, {s, 1, 15}]]], 70]

Crossrefs

Cf. A081053.

Sequence in context: A344883 A290001 A371422 * A135739 A096923 A141642

Adjacent sequences: A080690 A080691 A080692 * A080694 A080695 A080696

Keyword

nonn

Author

Mario Maqueda Garcia [Garci'a] (israelmira(AT)terra.es), Mar 03 2003

Extensions

Edited and extended by Robert G. Wilson v, Mar 05 2003

Status

approved