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A245321 Sum of digits of n written in fractional base 6/5. 1
0, 1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 9, 10, 11, 12, 13, 14, 12, 13, 14, 15, 16, 17, 14, 15, 16, 17, 18, 19, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 25, 19, 20, 21, 22, 23, 24, 23, 24, 25, 26, 27, 28, 21, 22, 23, 24, 25, 26, 24, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The base 6/5 expansion is unique and thus the sum of digits function is well-defined.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A007953(A024638(n)).

EXAMPLE

In base 6/5 the number 15 is represented by 543 and so a(15) = 5 + 4 + 3 = 12.

MAPLE

a:= proc(n) `if`(n<1, 0, irem(n, 6, 'q')+a(5*q)) end:

seq(a(n), n=0..100);  # Alois P. Heinz, Aug 19 2019

MATHEMATICA

a[n_]:= a[n] = If[n==0, 0, a[5*Floor[n/6]] + Mod[n, 6]]; Table[a[n], {n, 0, 70}] (* G. C. Greubel, Aug 19 2019 *)

PROG

(Sage)

def basepqsum(p, q, n):

....L=[n]

....i=1

....while L[i-1]>=p:

........x=L[i-1]

........L[i-1]=x.mod(p)

........L.append(q*floor(x/p))

........i+=1

....return sum(L)

[basepqsum(6, 5, i) for i in [0..70]]

CROSSREFS

Cf. A000120, A007953, A024638, A053827, A244040.

Sequence in context: A247973 A195181 A003005 * A006163 A053757 A256562

Adjacent sequences:  A245318 A245319 A245320 * A245322 A245323 A245324

KEYWORD

nonn,base

AUTHOR

Tom Edgar, Jul 18 2014

STATUS

approved

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Last modified December 5 20:40 EST 2019. Contains 329777 sequences. (Running on oeis4.)