A254311 Set of all natural numbers m such that m < S(m), where the function S is as defined in A257480.

3, 7, 11, 15, 19, 23, 27, 31, 32, 35, 39, 43, 47, 51, 55, 59, 63, 64, 67, 71, 75, 79, 83, 87, 91, 95, 96, 99, 103, 107, 111, 115, 119, 123, 127, 128, 131, 135, 139, 143, 147, 151, 155, 159, 160, 163, 167, 170, 171, 175, 179, 183, 187, 191, 192, 195, 199, 203

Offset: 1

Author

L. Edson Jeffery, May 03 2015

Keywords

• nonn

Comments

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.

Conjecture: A254312 is a permutation of this sequence.

Crossrefs

Cf. A254312, A257480.

Programs

Mathematica

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