A079206 Numbers n in which the first K digits of n form an integer divisible by the K-th prime, for K = 1, 2, ..., M, where M is the number of digits in n.

2, 4, 6, 8, 21, 24, 27, 42, 45, 48, 60, 63, 66, 69, 81, 84, 87, 210, 215, 240, 245, 270, 275, 420, 425, 450, 455, 480, 485, 600, 605, 630, 635, 660, 665, 690, 695, 810, 815, 840, 845, 870, 875, 2100, 2107, 2156, 2401, 2408, 2450, 2457, 2702, 2709, 2751, 2758

Offset

1,1

Comments

There are 200 terms in the sequence and 10-digit number 8757193191 is the largest number to satisfy the requirements. - Shyam Sunder Gupta, Aug 04 2013

Links

Shyam Sunder Gupta, Table of n, a(n) for n = 1..200

Divisible by Primes (missing)

Example

a(88)=21076 because 2 is divisible by the first prime 2, 21 by the second prime 3, 210 by the third prime 5, 2107 by the fourth prime 7, 21076 by the fifth prime 11.

Mathematica

a = Table[j, {j, 2, 8, 2}]; r = 2; t = a; While[! a == {}, n = Length[a]; k = 1; b = {}; While[! k > n, z0 = a[[k]]; Do[z = 10*z0 + j; If[Mod[z, Prime[r]] == 0, b = Append[b, z]; t = Append[t, z]], {j, 0, 9}]; k++]; a = b; r++]; t (* Shyam Sunder Gupta, Aug 04 2013 *)

Prog

(Python)
P, R, m = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37], [2, 4, 6, 8], 1
a = R[:]
while len(R) > 0:
    R = [t for t in (10*q+d for q in R for d in range(10)) if t%P[m]==0]
    a, m = a + R, m+1
print(a) # Michael S. Branicky, Feb 02 2024

Crossrefs

Sequence in context: A335209 A119261 A062285 * A265342 A335661 A230105

Adjacent sequences: A079203 A079204 A079205 * A079207 A079208 A079209

Keyword

base,fini,full,nonn

Author

Sudipta Das (juitech(AT)vsnl.net), Feb 03 2003

Status

approved