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

1, 2, 3, 4, 5, 6, 7, 8, 21, 24, 42, 110, 114, 120, 162, 192, 201, 220, 320, 330, 342, 372, 510, 511, 522, 552, 700, 774, 912, 954, 960, 1010, 1014, 1015, 1020, 1050, 1088, 1092, 1101, 1104, 1122, 1242, 1270, 1300, 1410, 1422, 1458, 1526, 1584, 1590, 1602, 1632

Offset: 1

Author

John Bibby, Mar 16 2024

Keywords

• nonn
• base

Examples

			The three consecutive Harshad numbers starting at 8 (8, 9, 10) are in arithmetic progression.
The same is true of the three consecutive Harshad numbers starting at 21 (21, 24, 27).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005349, A122535, A154701 (subsequence).

Programs

Mathematica

Select[Partition[Select[Range[2000], Divisible[#, DigitSum[#]] &], 3, 1], Equal @@ Differences[#] &][[;;, 1]] (* Amiram Eldar, Mar 17 2024 *)

Python

from itertools import count, islice
def agen(): # generator of terms
    h1, h2, h3 = 1, 2, 3
    while True:
        if h3 - h2 == h2 - h1: yield h1
        h1, h2, h3 = h2, h3, next(k for k in count(h3+1) if k%sum(map(int, str(k))) == 0)
print(list(islice(agen(), 52))) # Michael S. Branicky, Mar 16 2024