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A063012 Sum of distinct powers of 20; i.e. numbers with digits in {0,1) base 20; i.e. write n in base 2 and read as if written in base 20. 2
0, 1, 20, 21, 400, 401, 420, 421, 8000, 8001, 8020, 8021, 8400, 8401, 8420, 8421, 160000, 160001, 160020, 160021, 160400, 160401, 160420, 160421, 168000, 168001, 168020, 168021, 168400, 168401, 168420, 168421, 3200000, 3200001, 3200020 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = a(n-2^[log2(n)])+20^[log2(n)]. a(2n) = 20*a(n); a(2n+1) = a(2n)+1 = 20*a(n)+1.

G.f.: (1/(1 - x))*Sum_{k>=0} 20^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

EXAMPLE

a(5) = 401 since 5 written in base 2 is 101 so a(5) = 1*20^2+0*20^1+1*20^0 = 400+0+1 = 401

a(n)=Sum_k>=0 {A030308(n,k)*A009964(k)}. - From Philippe Deléham, Oct 15 2011.

MATHEMATICA

Table[FromDigits[IntegerDigits[n, 2], 20], {n, 0, 40}] (* Harvey P. Dale, Jul 21 2014 *)

PROG

(PARI) baseE(x, b)= { local(d, e, f); e=0; f=1; while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } baseI(x, b)= { local(d, e, f); e=0; f=1; while (x>0, d=x-10*(x\10); x\=10; e+=d*f; f*=b); return(e) } { for (n=0, 1000, write("b063012.txt", n, " ", baseI(baseE(n, 2), 20)) ) } [From Harry J. Smith, Aug 15 2009]

CROSSREFS

A001477, A005836, A000695, A033042, A033043, A033044, A033045, A033046, A007088, A033047, A033048, A033049, A033050, A033051, A033052 are similar sequences for 2-16. Cf. A063013 for something similar in a different way.

Sequence in context: A219798 A063013 A028931 * A041836 A041837 A041838

Adjacent sequences:  A063009 A063010 A063011 * A063013 A063014 A063015

KEYWORD

easy,nonn,base

AUTHOR

Henry Bottomley, Jul 04 2001

EXTENSIONS

Edited by Charles R Greathouse IV, Aug 02 2010

STATUS

approved

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Last modified June 25 12:02 EDT 2017. Contains 288710 sequences.