cp's OEIS Frontend

A338852 a(n) = (7*floor(a(n-1)/3)) + (a(n-1) mod 3) with a(1) = 3.

%I A338852 #30 Dec 13 2020 06:19:44
%S A338852 3,7,15,35,79,183,427,995,2319,5411,12623,29451,68719,160343,374131,
%T A338852 872971,2036931,4752839,11089955,25876559,60378635,140883479,
%U A338852 328728115,767032267,1789741955,4176064559,9744150635,22736351479,53051486783
%N A338852 a(n) = (7*floor(a(n-1)/3)) + (a(n-1) mod 3) with a(1) = 3.
%C A338852 Maximum reduction height sequence for a (7,3) counter.
%H A338852 ARITH Project, <a href="http://www.aoki.ecei.tohoku.ac.jp/arith/mg/algorithm.html#ppa_73">7/3 counter</a>, Aoki lab., Tohoku University.
%H A338852 HandWiki, <a href="https://handwiki.org/wiki/Dadda_multiplier">Dadda Multiplier</a>
%H A338852 Stenzel, Kubitz and Garcia, <a href="https://www.ece.ucdavis.edu/~vojin/CLASSES/EPFL/Papers/4_Stenzel_mult_77.pdf">A Compact High-Speed Parallel Multiplication Scheme</a>, in IEEE Transactions on Computers, vol. C-26, no. 10, pp. 948-957, Oct. 1977, doi: 10.1109/TC.1977.1674730. See p. 137.
%e A338852 a(6) = 7*floor(79/3) + mod(79/3) = 183.
%t A338852 NestList[7 Floor[#/3] + Mod[#, 3] &, 3, 28] (* _Michael De Vlieger_, Nov 12 2020 *)
%o A338852 (C) int a(int n) {
%o A338852         int t1 = 3, nextTerm;
%o A338852         for (int i = 2; i <= n; ++i) {
%o A338852             nextTerm = 7*(t1/3) + t1%3;
%o A338852             t1 = nextTerm;
%o A338852         }
%o A338852         return t1;
%o A338852     }
%o A338852 (PARI) a(n) = if (n==1, 3, my(x=divrem(a(n-1), 3)); 7*x[1] + x[2]); \\ _Michel Marcus_, Nov 12 2020
%Y A338852 Cf. A061418.
%K A338852 nonn
%O A338852 1,1
%A A338852 _Chinmaya Dash_, Nov 12 2020