A053836 -id:A053836 - cp's OEIS frontend

A241989 Positive numbers n that are divisible by the sum of the digits of n in base 16.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 30, 32, 33, 35, 36, 40, 45, 48, 50, 54, 60, 64, 65, 66, 70, 72, 75, 80, 90, 96, 99, 100, 105, 108, 112, 120, 126, 128, 130, 132, 135, 140, 144, 150, 160, 165, 175, 176, 180, 192, 195, 198, 200

Offset: 1

Chai Wah Wu, Aug 22 2014

A base 16 version of Harshad (or Niven) numbers (A005349).

Numbers n such that n = 0 modulo A053836(n). - Antti Karttunen, Aug 22 2014

			82478 is in the sequence as it is 1422E in hexadecimal and 1+4+2+2+14 = 23 which divides 82478.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A005349, A053836, A245802.

Select[Range[200], Divisible[#, Total@ IntegerDigits[#, 16]] &] (* Indranil Ghosh, Jun 12 2017 *)

from gmpy2 import digits
A241989 = [n for n in range(1,10**3) if not n % sum([int(d,16) for d in digits(n,16)])]
(MIT/GNU Scheme, with Antti Karttunen's IntSeq-library)
(define A241989 (MATCHING-POS 1 1 (lambda (n) (zero? (modulo n (A053836 n))))))
(define (A053836 n) (let loop ((n n) (i 0)) (if (zero? n) i (loop (floor->exact (/ n 16)) (+ i (modulo n 16))))))

A135738 Least positive integer with even digit sum in bases 2..n.

Original entry on oeis.org

3, 6, 10, 10, 54, 54, 54, 54, 130, 130, 130, 130, 390, 390, 2000, 2000, 3238, 3238, 4080, 4080, 7326, 7326, 16584, 16584, 17310, 17310, 17310, 17310, 17310, 17310, 17310, 17310, 231000, 231000, 231000, 231000, 466352, 466352, 466352, 466352, 3020830

Offset: 2

M. F. Hasler, Dec 06 2007

The sequence is obviously increasing. It seems that a(2n+1) = a(2n) for n > 1. Is there a simple proof? Is there a simple way to construct a(n)? Notice the pattern in base N, e.g., 130 = 10000010_2 = 11211_3 = 2002_4 = 1010_5 = 334_6 = 244_7 = 202_8 = 154_9 = 109_11 = {10}{10}_12 = {10}0_13.

			a(2)=3 since 1=1_2, 2=10_2, so 3=11_2 is the number > 0 with even digit sum (1+1) in base 2.
a(3)=6 since 4=100_2, 5=12_3, so 6=20_3=110_2 is the least N > 0 with even digit sum in base 2 and in base 3.
a(4)=a(5)=10=1010_2=101_3=22_4=20_5 is the least N > 0 having even digit sum in bases 2 through 4 and has so also in base 5.

"Davar55" on mersenneforum.org, Puzzles / "Sum of digits".

Cf. A000120, A053735, A053737, A053824, A053827-A053836, A007953.

digitsum(n,b=10,s)={n=[n];while(n=divrem(n[1],b),s+=n[2]);s}
A135738(Bmax,n=1)={until(!n++,for(b=2,Bmax,digitsum(n,b)%2&next(2));return(n))} /* n-th element of the sequence */
t=1;for(b=2,100,print(b,":",t=A135738(b,t))) /* display the list */

Corrected example a(3)=5 to a(3)=6 David Yablon (davar55(AT)yahoo.com), Mar 19 2010

cp's OEIS Frontend

A241989 Positive numbers n that are divisible by the sum of the digits of n in base 16.

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