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

1,2

Links

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

Cf. A005349, A122535, A154701 (subsequence).

Sequence in context: A366838 A236836 A134942 * A215888 A240963 A053408

Adjacent sequences: A371257 A371258 A371259 * A371261 A371262 A371263

Keyword

nonn,base

Author

John Bibby, Mar 16 2024

Status

approved