

A254311


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


3



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
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OFFSET

1,1


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.


LINKS



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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



