A152210 a(1)=1; thereafter a(n) is smallest number > a(n-1) such that the sum a(1)+...+a(n) divides the concatenation a(1)...a(n).

1, 2, 6, 250488, 279786, 1060566, 1414088, 1767610, 2447460, 10031652, 10356624, 50373066, 155962698, 193715622, 375287934, 759659778, 3125214762, 3252158280, 21173281128, 22937721222, 104101965546, 164092928742, 284358161736

Offset

1,2

Comments

See A151995 for the nonmonotonic version.

Links

Table of n, a(n) for n=1..23.

Example

1+2 (=3) divides 12 --> HIT
1+2+3 (=6) does not divide 123
1+2+4 (=7) does not divide 124
1+2+5 (=8) does not divide 125
1+2+6 (=9) divides 126 --> HIT
...

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    an, s, c = 1, 1, "1"
    while True:
        yield an
        an = next(k for k in count(an+1) if int(c+str(k))%(s+k) == 0)
        s, c = s+an, c+str(an)
print(list(islice(agen(), 11))) # Michael S. Branicky, Apr 21 2026

Crossrefs

Cf. A151995, A166064, A165770, A165771.

Sequence in context: A135408 A165710 A151995 * A206034 A299376 A364750

Adjacent sequences: A152207 A152208 A152209 * A152211 A152212 A152213

Keyword

nonn,base,more

Author

N. J. A. Sloane, Oct 07 2009, based on a posting to the Sequence Fans Mailing List by Eric Angelini, Sep 29 2009

Extensions

Corrected by Zak Seidov, Oct 08 2009

a(14)-a(20) from Donovan Johnson, Jul 20 2010

a(21)-a(23) from Max Alekseyev, Jun 18 2011

Status

approved