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
Examples
(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.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..554
- Index entries for linear recurrences with constant coefficients, signature (65,-64).
Programs
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Maple
seq((10*64^(n-1)-1)/3, n=1..13); # Georg Fischer, Apr 10 2024
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Mathematica
Array[(10*64^(# - 1) - 1)/3 &, 13] (* Michael De Vlieger, Apr 10 2024 *)
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]
Extensions
More terms from Henry Bottomley, Dec 02 2002