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A371260 a(n) is the first of three consecutive Harshad numbers in arithmetic progression.

%I A371260 #33 Apr 06 2024 22:01:11
%S A371260 1,2,3,4,5,6,7,8,21,24,42,110,114,120,162,192,201,220,320,330,342,372,
%T A371260 510,511,522,552,700,774,912,954,960,1010,1014,1015,1020,1050,1088,
%U A371260 1092,1101,1104,1122,1242,1270,1300,1410,1422,1458,1526,1584,1590,1602,1632
%N A371260 a(n) is the first of three consecutive Harshad numbers in arithmetic progression.
%H A371260 Michael S. Branicky, <a href="/A371260/b371260.txt">Table of n, a(n) for n = 1..10000</a>
%e A371260 The three consecutive Harshad numbers starting at 8 (8, 9, 10) are in arithmetic progression.
%e A371260 The same is true of the three consecutive Harshad numbers starting at 21 (21, 24, 27).
%t A371260 Select[Partition[Select[Range[2000], Divisible[#, DigitSum[#]] &], 3, 1], Equal @@ Differences[#] &][[;;, 1]] (* _Amiram Eldar_, Mar 17 2024 *)
%o A371260 (Python)
%o A371260 from itertools import count, islice
%o A371260 def agen(): # generator of terms
%o A371260     h1, h2, h3 = 1, 2, 3
%o A371260     while True:
%o A371260         if h3 - h2 == h2 - h1: yield h1
%o A371260         h1, h2, h3 = h2, h3, next(k for k in count(h3+1) if k%sum(map(int, str(k))) == 0)
%o A371260 print(list(islice(agen(), 52))) # _Michael S. Branicky_, Mar 16 2024
%Y A371260 Cf. A005349, A122535, A154701 (subsequence).
%K A371260 nonn,base
%O A371260 1,2
%A A371260 _John Bibby_, Mar 16 2024