A075483 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+63.

89, 25, 22, 22, 35, 20, 66, 30, 17, 38, 133, 27, 25, 40, 35, 30, 20, 25, 22, 38, 38, 133, 51, 27, 17, 40, 22, 30, 20, 35, 22, 95, 131, 33, 20, 25, 27, 22, 27, 66, 17, 27, 71, 45, 33, 48, 35, 89, 22, 33, 30, 30, 48, 22, 40, 30, 17, 61, 30, 64, 22, 22, 25, 84, 22, 22, 25, 33

Offset: 0

Author

Labos Elemer, Sep 24 2002

Keywords

• nonn

Comments

1stSubmergeLengths[=A074473] with initial values belonging to other residue classes modulo 64 are either listed in A075476-A075483 or can be easily determined. For 64k+2s the first sink below initial value is at 2nd iterate; for 64k+4s+1 the first submerge below initial value comes at 4th term of iteration list; finally if initial value is of 64k+4s+3 form or moreover initial value = 64k+r, r = 3, 11, 19, 23, 35, 43, 51, 55, then for all k first sink emerges at the 7th, 9th, 7th, 9th, 7th, 9th, 7th, 9th iterates, respectively.

Examples

			n=8: 64n + 63 = 575, the list = the 17th term 410 < 575 = initial value, so a(8)=17.
		

Crossrefs

Cf. A006370, A074472, A074473, A075476-A075482.

Programs

Mathematica

Table[Function[k, Length@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, k, # >= k &]][64 n - 1], {n, 120}] (* Michael De Vlieger, Feb 20 2017 *)

Formula

a(n) = A074473(64n + 63).