A075876 Values of m for which A075825(m) = 1.

0, 2, 4, 12, 52, 212, 852, 3412, 13652, 54612, 218452, 873812, 3495252, 13981012, 55924052, 223696212, 894784852, 3579139412

Offset

1,2

Comments

For n > 4 it appears that a(n) = 4*a(n-1) + 4.

From Robert Israel, Nov 08 2016: (Start)

By induction, we have for k >= 0:

A075825((10*4^k-7)/3) = 2^(k+1)

A075825((10*4^k-4)/3) = 1

A075825((10*4^k-1)/3) = 2^(k+1)+1

A075825((20*4^k-8)/3) = 2^(k+1)-1

A075825((20*4^k-5)/3) = 2^(k+1)+1

A075825((20*4^k-1)/3) = 2^(k+1)

In particular, this sequence contains b(k) = (10*4^k-4)/3 which is the solution of b(k) = 4*b(k-1)+4 with b(0) = 2.

The only terms <= 2*10^7 that are not of that form are 0 and 4. (End)

Links

Table of n, a(n) for n=1..18.

Prog

(Python) # uses code/imports in A075825()
[print(k, end=", ") for k, ak in enumerate(A075825()) if ak == 1]
# Michael S. Branicky, Jan 02 2026

Crossrefs

Cf. A075825.

Sequence in context: A030924 A030831 A058767 * A222470 A372347 A227037

Adjacent sequences: A075873 A075874 A075875 * A075877 A075878 A075879

Keyword

nonn,more

Author

John W. Layman, Oct 16 2002

Extensions

a(10)-a(14) from Robert Israel, Nov 08 2016

a(15)-a(16) from Sean A. Irvine, Mar 11 2025

a(17)-a(18) from Michael S. Branicky, Jan 02 2026

Status

approved