A374847 Numbers k which can be written as k = r+s where r and s are elements of the Collatz trajectory of k.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 78, 80, 81, 82, 84

Offset

1,1

Comments

A trajectory term can be used twice as r = s, so all even numbers are terms (trajectory first term k/2).

The odd terms, which become sparse with increasing size, form A374909.

Links

Markus Sigg, Table of n, a(n) for n = 1..10000

Example

2 is a term because its Collatz trajectory is {2, 1} and 2 = 1+1.
21 is not a term: its Collatz trajectory is T = { 21, 64, 32, 16, 8, 4, 2, 1 } and there are no r,s in T with 21 = r+s.

Prog

(PARI) is_A374847(k) = { my(T=List(), m=k); while(m>1, if(m%2==0, m=m/2, m=3*m+1); if(m<k, listput(T, m)); ); 	for(i=1, #T, for(j=i, #T, if(T[i]+T[j]==k, return(1)); )); return(0); }

Crossrefs

Cf. A374909.

Sequence in context: A250251 A138234 A324720 * A247756 A375758 A032520

Adjacent sequences: A374844 A374845 A374846 * A374848 A374850 A374851

Keyword

nonn

Author

Markus Sigg, Jul 22 2024

Status

approved