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%I #17 Nov 13 2015 12:03:29
%S 3,7,11,15,19,23,27,31,32,35,39,43,47,51,55,59,63,64,67,71,75,79,83,
%T 87,91,95,96,99,103,107,111,115,119,123,127,128,131,135,139,143,147,
%U 151,155,159,160,163,167,170,171,175,179,183,187,191,192,195,199,203
%N Set of all natural numbers m such that m < S(m), where the function S is as defined in A257480.
%C Theorem: The sequence contains (i) a subset of equivalence class 0 modulo 4 comprising all numbers congruent to 0 modulo 32 and no others; (ii) no numbers congruent to 1 modulo 4; (iii) a subset of numbers congruent to 2 modulo 4; (iv) all numbers of congruence class 3 modulo 4.
%C Conjecture: A254312 is a permutation of this sequence.
%t max = 203; a = {}; v[x_] := IntegerExponent[x, 2]; f[x_] := (3*x + 1)/2^v[3*x + 1]; s[m_] := (3 + (3/2)^v[1 + f[4*m - 3]]*(1 + f[4*m - 3]))/6; Do[If[m < s[m], AppendTo[a, m]], {m, max}]; a
%Y Cf. A254312, A257480.
%K nonn
%O 1,1
%A _L. Edson Jeffery_, May 03 2015