A072196 Multiples of 3 which on one operation of the Collatz function T (N -> 3N+1/2^r) yield the number 5.

3, 213, 13653, 873813, 55924053, 3579139413, 229064922453, 14660155037013, 938249922368853, 60047995031606613, 3843071682022823253, 245956587649460688213, 15741221609565484045653, 1007438183012190978921813, 64476043712780222650996053, 4126466797617934249663747413, 264093875047547791978479834453

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..554

Index entries for linear recurrences with constant coefficients, signature (65,-64).

Formula

a(n) = (10*64^(n-1)-1)/3. - Henry Bottomley, Dec 02 2002 [Formula adapted to a change of offset by Georg Fischer, Apr 10 2024]

Example

(3*3+1)/2=5, (3*213+1)/2^7=5, etc. Thus multiples of 3 act as generators on the numbers in the Collatz domain.

Maple

seq((10*64^(n-1)-1)/3, n=1..13); # Georg Fischer, Apr 10 2024

Mathematica

Array[(10*64^(# - 1) - 1)/3 &, 13] (* Michael De Vlieger, Apr 10 2024 *)

Crossrefs

Cf. A139391, A072197.

Sequence in context: A063407 A303214 A258110 * A038785 A297920 A298544

Adjacent sequences: A072193 A072194 A072195 * A072197 A072198 A072199

Keyword

nonn,easy,changed

Author

N. Rathankar (rathankar(AT)yahoo.com), Jul 03 2002

Extensions

More terms from Henry Bottomley, Dec 02 2002

Status

approved