A260593 The values of the modified Syracuse algorithm, msa, in the order in which they appear in A260590.

4, 2, 7, 5, 59, 56, 8, 54, 51, 45, 42, 31, 15, 40, 21, 29, 13, 12, 20, 27, 24, 10, 16, 18, 23, 39, 81, 35, 37, 26, 80, 34, 78, 43, 32, 61, 58, 50, 48, 46, 70, 65, 69, 53, 64, 77, 73, 72, 105, 75, 67, 83, 62, 92, 135, 126, 86, 111, 129, 124, 123, 127, 88, 119, 108, 100

Offset: 1

Author

Joseph K. Horn and Robert G. Wilson v, Aug 30 2015

Keywords

• nonn
• easy

Comments

See A260590 for the definition of the msa.

Sorted: 2, 4, 5, 7, 8, 10, 12, 13, 15, 16, 18, 20, 21, 23, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 69, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 89, 91, 92, 94, 96, 97, 99, 100, ... (A020914(n) for n>0).

Record values: 4, 7, 59, 81, 105, 135, 164, 165, 173, 176, 183, 224, 246, 287, 292, 298, 308, 376, 395, 398, 433, 447, ... .

Record last values to appear: 2, 5, 8, 10, 16, 18, 23, 26, 32, 46, 53, 62, 85, 94, 99, 102, 107, 115, 118, 130, 132, 134, 148, ... .

Examples

			Every odd number greater than 1 yields a msa value. a(1) is 4 and it corresponds to A260590(1).
a(2) is 2 since A260590(2) is 2.
a(3) is 7 since A260590(3) is 7.
a(4) is 5 since A260590(5) is 5, A260590(4) is 2 but it already appears as a(2).
		

Crossrefs

Cf. A260590, A260594.

Programs

Mathematica

msa[n_] := If[ OddQ@ n, (3n + 1)/2, n/2]; f[n_] := Block[{k = 2n + 1}, Length@ NestWhileList[ msa@# &, k, # >= k &] - 1]; k = 1; lst = {}; While[k < 10000001, a = f@ k; If[ !MemberQ[lst, a], AppendTo[lst, a]]; k++]; lst