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

1,1

Comments

Values are tested for natural numbers up to 1000000.

References

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A070165, A070991.

Sequence in context: A331483 A342151 A070723 * A165863 A008941 A133897

Adjacent sequences: A221210 A221211 A221212 * A221214 A221215 A221216

Keyword

nonn

Author

Jayanta Basu, Feb 21 2013

Status

approved