A137366 Subsequence of A137365 where it is possible to choose p1, p2, p3 so that p1+p2+p3 = prime.

1483, 5381, 6271, 7229, 9181, 11897, 13103, 13841, 14489, 17107, 20357, 25747, 26711, 27917, 30161, 30259, 31247, 32579, 36677, 36899, 36901, 42083, 48817, 54181, 55511, 55691, 56377, 57637, 64151, 66347, 69389, 75167, 76031, 76123

Offset

1,1

Comments

36161 is the first number that is in A137365 but not in the present sequence. See A138556.

Links

R. J. Mathar and Vincenzo Librandi, Table of n, a(n) for n = 1..350 (first 44 terms from R. J. Mathar)

Example

1483=3^3+5^3+11^3, 3+5+11=17;
7229=3^3+7^3+19^3, 3+7+19=29.

Mathematica

Array[r, 99]; Array[y, 99]; For[i = 0, i < 10^2, r[i] = y[i] = 0; i++ ]; z = 4^2; n = 0; For[i1 = 1, i1 < z, a = Prime[i1]; a2 = a^3; For[i2 = i1 + 1, i2 < z, b = Prime[i2]; b2 = b^3; For[i3 = i2 + 1, i3 < z, c = Prime[i3]; c2 = c^3; p = a2 + b2 + c2; p3 = a + b + c; If[PrimeQ[p] && PrimeQ[p3], Print[a2, " + ", b2, " + ", c2, " = ", p, "; ", a, " + ", b, " + ", c, " = ", p3]; n++; r[n] = p]; i3++ ]; i2++ ]; i1++ ]; Sort[Array[r, 71]]
lst = {}; Do[q = Prime@a; r = Prime@b; s = Prime@c; p = q^3 + r^3 + s^3; t = q + r + s; If[PrimeQ@p && PrimeQ@t, AppendTo[lst, p]], {a, 14}, {b, a - 1}, {c, b - 1}]; Take[Sort@lst, 35] (* Robert G. Wilson v, Apr 13 2008 *)

Crossrefs

Cf. A137365, A138556.

Sequence in context: A035864 A255087 A137365 * A045008 A327880 A257713

Adjacent sequences: A137363 A137364 A137365 * A137367 A137368 A137369

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2008, Apr 14 2008

Status

approved