A065255 Consider the sequence b(k) such that b(k) and sigma(b(k)) end with the same digit in base 10. Sequence gives values of b(k) such that b(k)/k = 10.

40, 290, 600, 790, 1350, 1400, 4580, 4590, 4640, 4740, 4750, 9080, 9480, 9570, 9600, 11000, 11020, 11080, 11160, 11210, 11240, 11290, 11310, 11570, 11590, 11720, 11780, 11800, 13870, 13880, 13990, 14060, 14250, 14290, 14310, 14320, 14340, 14590, 14760, 15920, 16390

Offset

1,1

Comments

Conjecture: lim n -> infinity b(k)/k = 10.

Links

David A. Corneth, Table of n, a(n) for n = 1..249 (terms <= 10^9)

Example

b(k) begins 1,14,34,40,44,74,78,81,84 hence b(4)=40 and 40/4=10 so 40 is in the sequence.

Prog

(PARI) upto(n) = {my(b = List(), res = List(), t = 0); forfactored(i = 1, n, s = sigma(i[2]); if((s - i[1])%10 == 0, t++; if(10*t == i[1], listput(res, i[1])))); res} \\ David A. Corneth, Aug 23 2023

Crossrefs

Cf. A072566 (b).

Sequence in context: A334121 A117216 A035099 * A300920 A061993 A087954

Adjacent sequences: A065252 A065253 A065254 * A065256 A065257 A065258

Keyword

base,nonn

Author

Benoit Cloitre, Aug 06 2002

Extensions

Name corrected by Sean A. Irvine, Aug 23 2023

More terms from David A. Corneth, Aug 23 2023

Status

approved