A221213 Conjectured total number of times that k-n appears in the Collatz (3x+1) sequence of k for k = 1, 2, 3,....

42, 42, 57, 52, 46, 53, 58, 57, 54, 49, 56, 59, 49, 62, 61, 59, 69, 59, 50, 54, 72, 64, 65, 55, 57, 54, 55, 66, 61, 60, 62, 61, 64, 73, 62, 59, 71, 63, 62, 58, 68, 72, 63, 59, 57, 65, 70, 59, 60, 59, 71, 55, 64, 54, 66, 75, 67, 62, 64, 64, 73, 68, 68, 67, 58, 61

Offset: 1

Author

Jayanta Basu, Feb 21 2013

Keywords

• nonn

Comments

Values are tested for natural numbers up to 1000000.

Examples

			a(1) = 42 = total number of k such that k-1 appears in the Collatz sequence of k, that is, the number of terms in A070991.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, E16.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070165, A070991.

Programs

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 75; t = Table[0, {nn}]; lastChange = 10; k = 0; While[k < 2*lastChange, k++; c = Collatz[k]; d = Intersection[Range[nn], k - c]; If[Length[d] > 0, lastChange = k; t[[d]]++]]; t (* T. D. Noe, Feb 21 2013 *)