A219956 Numbers expressible as 2*p + 3*q in exactly in one way, where p and q are primes.

10, 12, 13, 15, 16, 20, 21, 23, 27, 28, 29, 32, 39, 40, 41, 44, 45, 52, 57, 63, 64, 68, 75, 80, 88, 92, 93, 99, 100, 112, 117, 124, 128, 129, 135, 140, 147, 148, 152, 164, 165, 172, 183, 184, 189, 200, 207, 208, 212, 219, 220, 224, 225, 232, 243, 255, 260

Offset

1,1

Comments

Sequence is infinite: All integers of the forms either 2*prime or 3*prime plus 6 are here.

Suggestion: all odd terms are multiples of 3 except for four primes 13, 23, 29, 41.

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Example

10 = 2*2 + 3*2, 12 = 2*3 + 3*2, 13 = 2*2 + 3*3.

Mathematica

mx = 260; Sort[First /@ Select[Tally[ Flatten@Table[2 Prime[i] + 3 Prime[k], {k, PrimePi[(mx - 4)/3]}, {i, PrimePi[(mx - 3 Prime[k])/2]}]], #[[2]] < 2 &]]

Prog

(PARI) list(lim)=my(v=vectorsmall(lim\1), u=List()); forprime(p=2, lim\2, forprime(q=2, (lim-2*p)\3, v[2*p+3*q]++)); for(i=1, #v, if(v[i]==1, listput(u, i))); Vec(u) \\ Charles R Greathouse IV, Dec 05 2012

Crossrefs

Cf. A079026, A219955.

Sequence in context: A031288 A127957 A079026 * A331276 A230597 A330904

Adjacent sequences: A219953 A219954 A219955 * A219957 A219958 A219959

Keyword

nonn

Author

Zak Seidov, Dec 02 2012

Status

approved