A139436 Number of ways to write n as sum of initial terms of a Collatz trajectory starting with a value less than n.

0, 0, 1, 0, 1, 1, 3, 1, 2, 1, 1, 2, 2, 4, 3, 1, 1, 3, 3, 1, 7, 2, 1, 3, 1, 2, 2, 5, 4, 3, 4, 1, 4, 2, 7, 5, 3, 2, 3, 5, 1, 9, 5, 2, 6, 3, 3, 4, 8, 4, 5, 5, 4, 6, 5, 8, 5, 3, 5, 7, 5, 5, 11, 5, 3, 7, 6, 4, 7, 10, 6, 4, 7, 6, 6, 6, 11, 6, 4, 7, 6, 5, 5, 14, 6, 3, 7, 8, 4, 7, 16, 5, 6, 6, 7, 5, 5, 12, 8, 3, 7, 7

Offset

1,7

Comments

a(n) = 0 iff A139435(n) = 0; a(n) > 0 for n > 4;

a(A139437(n)) = 1.

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Collatz Problem

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

a(10) = #{2+1+4+2+1} = 1;
a(11) = #{4+2+1+4} = 1;
a(12) = #{1+4+2+1+4,8+4} = 2;
a(13) = #{4+2+1+4+2,3+10} = 2;
a(14) = #{1+4+2+1+4+2,2+1+4+2+1+4,4+2+1+4+2+1,8+4+2} = 4;
a(15) = #{1+4+2+1+4+2+1,8+4+2+1,10+5} = 3.

Crossrefs

Cf. A006370.

Sequence in context: A098872 A349473 A167366 * A212305 A205555 A165913

Adjacent sequences: A139433 A139434 A139435 * A139437 A139438 A139439

Keyword

nonn

Author

Reinhard Zumkeller, Apr 21 2008

Status

approved