A151995 a(1)=1; thereafter a(n) is smallest positive number not already in the sequence such that the sum a(1)+...+a(n) divides the concatenation a(1)...a(n).

1, 2, 6, 250488, 19986, 118030, 133970, 693810, 2231328, 3407286, 5733260, 25176334, 75529002, 1913932644, 2692452, 5413116264, 6766395330, 2492882490, 9544178676, 19819882608, 10086515692, 10541120510, 4147755864, 6025730266

Offset

1,2

Links

Table of n, a(n) for n=1..24.

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
...
126250488 == (1+2+6+250488) * 504
...
The sum of the first 14 terms, 2027226147, divides their concatenation
1262504881998611803013397069381022313283407286573326025176334755290021913932644,
giving a quotient of
622774565071062988323520804204101612390759720490782533881916606559052.

Maple

g:= proc() local d, Q;
  for d from 1 do
     Q:= select(y -> y >= 10^(d-1)+s and y < 10^d + s, NumberTheory:-Divisors(10^d*c-s)) minus S;
     if Q <> {} then return min(Q) - s fi
  od
end proc:
s:= 1: c:= 1: R:= 1: S:= {1}:
for n from 2 to 15 do
  x:= g(); s:= s + x; c:= 10^(1+ilog10(x))*c + x; S:= S union {x}; R:= R, x;
od:
R; # Robert Israel, Apr 21 2026

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(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. A152210, A166064, A165770, A165771.

Sequence in context: A161563 A135408 A165710 * A152210 A206034 A299376

Adjacent sequences: A151992 A151993 A151994 * A151996 A151997 A151998

Keyword

nonn,base

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

More terms from Jack Brennen, John W. Layman, Charles R Greathouse IV and Robert G. Wilson v, Sep 30 2009. Jack Brennen found a(14).

Definition corrected by Zak Seidov, Oct 08 2009

a(15)-a(24) from Donovan Johnson, Jul 20 2010

Status

approved