A284814 Least number k such that k mod (2, 3, 4, ... , n+1) = (d_1, d_2, ..., d_n), where d_1 , d_2, …, d_n are the digits of n, with MSD(n) = d_1 and LSD(n) = d_n. 0 if such a number does not exist.

1, 0, 0, 0, 11311, 0, 1032327, 11121217, 101033565, 0, 10333633323, 0, 0, 11121314781937, 0

Offset

1,5

Comments

Suggested by Francis Maleval in Linkedin "Number Theory" group.

Links

Table of n, a(n) for n=1..15.

Example

a(11) = 10333633323 because:
10333633323 mod 2 = 1, 10333633323 mod 3 = 0, 10333633323 mod 4 = 3,
10333633323 mod 5 = 3, 10333633323 mod 6 = 3, 10333633323 mod 7 = 6,
10333633323 mod 8 = 3, 10333633323 mod 9 = 3, 10333633323 mod 10 = 3,
10333633323 mod 11 = 2, 10333633323 mod 12 = 3.

Maple

P:=proc(q) local a, d, j, k, n, ok; for k from 1 to q do d:=0; for n from 10^(k-1) to 10^k-1 do
ok:=1; a:=n; for j from 1 to ilog10(n)+1 do if (a mod 10)<>n mod ((ilog10(n)+2-j)+1)
then ok:=0; break; else a:=trunc(a/10); fi; od; if ok=1 then print(n); d:=1; break; fi; od;
if n=10^k and d=0 then print(0); fi; od; end: P(20);

Crossrefs

Cf. A284815.

Sequence in context: A112441 A104017 A317400 * A228627 A178581 A178583

Adjacent sequences: A284811 A284812 A284813 * A284815 A284816 A284817

Keyword

nonn,base,hard,more

Author

Paolo P. Lava, Apr 10 2017

Extensions

a(12)-a(15) from Giovanni Resta, Apr 10 2017

Status

approved