A266181 Numbers k such that k == d_1 (mod 2), k == d_2 (mod 3), k == d_3 (mod 4) etc., where d_1 d_2 d_3 ... is the decimal expansion of k.

1, 11311, 1032327, 1210565, 11121217, 101033565, 111214177, 113411719, 121254557, 123254387, 10333633323, 12105652565, 11121314781937

Offset

1,2

Comments

Subsequence of A131835, the numbers starting with 1. - Michel Marcus, Dec 30 2015

If it exists, a(14) >= 10^21. - Hiroaki Yamanouchi, Jan 12 2016

Definition assumes that d_i are residues, as otherwise 2,3,...,9 are also terms. - Chai Wah Wu, Jun 23 2020

Links

Table of n, a(n) for n=1..13.

Example

11311 == 1 (mod 2),
11311 == 1 (mod 3),
11311 == 3 (mod 4),
11311 == 1 (mod 5),
11311 == 1 (mod 6).

Mathematica

Select[Range@ 2000000, First@ Union@ Function[k, MapIndexed[Mod[k, First@ #2 + 1] == #1 &, IntegerDigits@ k]]@ # &] (* Michael De Vlieger, Dec 30 2015 *)

Prog

(Python)
for b in range (3, 11):
    for i in range (10**(b-2), 13*10**(b-3)):
        si, k, kk=str(i), 0, i
        for j in range(1, b):
            if int(si[len(str(i))-j])==kk%(b+1-j):
                k=k+1
        if k==len(str(i)):
            print (i)
(Python)
def ok(n): return all(n%i == di for i, di in enumerate(map(int, str(n)), 2)) # Michael S. Branicky, Jan 21 2025
(PARI) isok(n) = {my(d = digits(n)); for (i=1, #d, if (n % (i+1) != d[i], return (0)); ); return (1); } \\ Michel Marcus, Dec 30 2015

Crossrefs

Cf. A131835.

Sequence in context: A178581 A178583 A178589 * A179917 A287245 A067791

Adjacent sequences: A266178 A266179 A266180 * A266182 A266183 A266184

Keyword

nonn,base,more,changed

Author

Pieter Post, Dec 29 2015

Extensions

a(6)-a(12) from Michel Marcus, Dec 30 2015

a(13) from Hiroaki Yamanouchi, Jan 12 2016

Status

approved