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

%I A091629 #49 Aug 27 2025 12:03:10
%S A091629 6,12,24,48,96,192,384,768,1536,3072,6144,12288,24576,49152,98304,
%T A091629 196608,393216,786432,1572864,3145728,6291456,12582912,25165824,
%U A091629 50331648,100663296,201326592,402653184,805306368,1610612736,3221225472
%N A091629 Product of digits associated with A091628(n). Essentially the same as A007283.
%C A091629 Sequence arising in _Farideh Firoozbakht_'s solution to Prime Puzzle 251 - 23 is the only pointer prime (A089823) not containing digit "1".
%C A091629 The monotonic increasing value of successive product of digits strongly suggests that in successive n the digit 1 must be present.
%H A091629 G. C. Greubel, <a href="/A091629/b091629.txt">Table of n, a(n) for n = 1..1000</a>
%H A091629 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A091629 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_251.htm">Puzzle 251, Pointer primes</a>, The Prime Puzzles and Problems Connection.
%H A091629 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F A091629 a(n) = 3 * 2^n = product of digits of A091628(n).
%F A091629 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A091629 a(n) = 6*2^(n-1).
%F A091629 a(n) = 2*a(n-1), with a(1) = 6.
%F A091629 G.f.: 6*x/(1-2*x). (End)
%F A091629 E.g.f.: 3*(exp(2*x) - 1). - _G. C. Greubel_, Jan 05 2023
%t A091629 3*2^Range[1, 60] (* _Vladimir Joseph Stephan Orlovsky_, Jun 09 2011 *)
%o A091629 (Magma) [3*2^n : n in [1..40]]; // _Wesley Ivan Hurt_, Jul 17 2020
%o A091629 (SageMath) [3*2^n for n in range(1,51)] # _G. C. Greubel_, Jan 05 2023
%Y A091629 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).
%Y A091629 Cf. A089823, A091628, A091630, A091631, A091632.
%Y A091629 Similar to A003945, A042950, A058764, A087009, A081808.
%K A091629 base,easy,nonn,changed
%O A091629 1,1
%A A091629 _Enoch Haga_, Jan 24 2004
%E A091629 Edited and extended by _Ray Chandler_, Feb 07 2004