A137366 - OEIS

%I #14 Mar 05 2024 14:46:42

%S 1483,5381,6271,7229,9181,11897,13103,13841,14489,17107,20357,25747,

%T 26711,27917,30161,30259,31247,32579,36677,36899,36901,42083,48817,

%U 54181,55511,55691,56377,57637,64151,66347,69389,75167,76031,76123

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

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

%H R. J. Mathar and Vincenzo Librandi, <a href="/A137366/b137366.txt">Table of n, a(n) for n = 1..350</a> (first 44 terms from R. J. Mathar)

%e 1483=3^3+5^3+11^3, 3+5+11=17;

%e 7229=3^3+7^3+19^3, 3+7+19=29.

%t 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]]

%t 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 *)

%Y Cf. A137365, A138556.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 09 2008, Apr 14 2008