A121669 Numbers with sum of digits = 19, divisible by 19 and containing the string "19".

17119, 19171, 19342, 19513, 20197, 21907, 33193, 34219, 41914, 51319, 61921, 101935, 102619, 112195, 119035, 119206, 121942, 125191, 171019, 171190, 190171, 190342, 190513, 191026, 191710, 192052, 192223, 193420, 194104, 195130, 195301, 197011, 201970, 204193

Offset: 1

Author

Hassan Taifour (hytaifour(AT)yahoo.co.uk), Sep 10 2006

Keywords

• nonn
• base

Comments

Conjecture: There are approximately k(n-1)(n-2)^(n-2) terms of this sequence up to 10^n, where k is about e/(19e-19). - Charles R Greathouse IV, Oct 13 2022

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..12794 (all terms < 10^11)

Crossrefs

Intersection of A008601, A166459 and A293879.

Programs

Mathematica

d19Q[n_]:=Module[{idn=IntegerDigits[n]},Total[idn]==19&&MemberQ[ Partition[ idn,2,1],{1,9}]]; Select[19*Range[20000],d19Q] (* Harvey P. Dale, Jun 10 2014 *)

Python

def ok(n): s = str(n); return n%19==0 and '19' in s and sum(map(int, s))==19
print(list(filter(ok, range(205000)))) # Michael S. Branicky, Aug 06 2021

Extensions

More terms from Zak Seidov, Sep 12 2006