A091629 Product of digits associated with A091628(n). Essentially the same as A007283.

6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472

Offset: 1

Author

Enoch Haga, Jan 24 2004

Keywords

• base
• easy
• nonn
• changed

Comments

Sequence arising in Farideh Firoozbakht's solution to Prime Puzzle 251 - 23 is the only pointer prime (A089823) not containing digit "1".

The monotonic increasing value of successive product of digits strongly suggests that in successive n the digit 1 must be present.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Tanya Khovanova, Recursive Sequences
• Carlos Rivera, Puzzle 251, Pointer primes, The Prime Puzzles and Problems Connection.
• Index entries for linear recurrences with constant coefficients, signature (2).

Crossrefs

Sequences of the form (2*m+1)*2^n: A000079 (m=0), A007283 (m=1), A020714 (m=2), A005009 (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), A110287 (m=8), A110288 (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).

Cf. A089823, A091628, A091630, A091631, A091632.

Similar to A003945, A042950, A058764, A087009, A081808.

Programs

Magma

[3*2^n : n in [1..40]]; // Wesley Ivan Hurt, Jul 17 2020

Mathematica

3*2^Range[1, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)

SageMath

[3*2^n for n in range(1,51)] # G. C. Greubel, Jan 05 2023

Formula

a(n) = 3 * 2^n = product of digits of A091628(n).

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 6*2^(n-1).

a(n) = 2*a(n-1), with a(1) = 6.

G.f.: 6*x/(1-2*x). (End)

E.g.f.: 3*(exp(2*x) - 1). - G. C. Greubel, Jan 05 2023

Extensions

Edited and extended by Ray Chandler, Feb 07 2004