login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238088 a(n) is the smallest k > 0 such that the first n multiples of k have the same sum of digits, but (n+1)k has a different one. a(n)=0 if no such k exists. 2
1, 63, 72, 135, 81, 27, 36, 1881, 0, 9, 549, 1683, 1782, 3465, 1728, 1287, 1386, 891, 0, 1188, 95904, 693, 87912, 204795, 81918, 42957, 73926, 792, 0, 40959, 65934, 36963, 67932, 1485, 61938, 297, 53946, 28971, 0, 30969, 1881198, 26973, 47952, 114885, 4419558 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(10*t-1) = 0 for t > 0, because if the first 10*t-1 multiples of a number k have the same sum of digits, then 10*t*k also has the same sum, since sod(10*t*k) = sod(t*k).

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000

EXAMPLE

a(4) = 135 since 1*135 = 135, 2*135 = 270, 3*135 = 405 and 4*135 = 540 all have the same sum of digits (9) while 5*135 = 675 has a different sum of digits.

MATHEMATICA

sod[n_] := Plus @@ IntegerDigits@n; okQ[n_, k_] := Catch@Block[{s = sod@k}, Do[If[ sod[j*k] != s, Throw@ False], {j, 2, n}]; sod[k*(n + 1)] != s]; a[n_] := If[ Mod[n, 10] == 9, 0, Block[{k = 1}, While[! okQ[n, k], k++]; k]]; Array[a, 20]

PROG

(PARI) for(r=2, 46, n=0; if(Mod(r, 10)==0, print1(n, ", "), until(m==r, n++; s=sumdigits(n); m=1; until(!(sumdigits(n*m)==s), m++)); print1(n, ", "))); \\ Arkadiusz Wesolowski, Feb 21 2014

CROSSREFS

Cf. A007953, A237994.

Sequence in context: A095543 A347944 A073569 * A046049 A240528 A320066

Adjacent sequences:  A238085 A238086 A238087 * A238089 A238090 A238091

KEYWORD

nonn,base

AUTHOR

Giovanni Resta, Feb 17 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 13:05 EST 2021. Contains 349563 sequences. (Running on oeis4.)