A284815 Least number k such that k mod (2, 3, 4, ... , n+1) = (d_n, d_n-1, ..., d_1), where d_1 , d_2, ..., d_n are the digits of k, with MSD(k) = d_1 and LSD(k) = d_n. 0 if such a number does not exist.

1, 10, 0, 1101, 11311, 340210, 4620020, 12040210, 151651121, 1135531101, 0, 894105331101, 0, 15379177511311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Formula

Conjecture: a(n) = 0 for all n >= 15. - Max Alekseyev, Nov 10 2022

Example

a(7) = 4620020 because:
4620020 mod 2 = 0, 4620020 mod 3 = 2, 4620020 mod 4 = 0,
4620020 mod 5 = 0, 4620020 mod 6 = 2, 4620020 mod 7 = 6,
4620020 mod 8 = 4.

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 (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

Sequence in context: A286018 A286646 A104013 * A286116 A286082 A286730

Adjacent sequences: A284812 A284813 A284814 * A284816 A284817 A284818

Keyword

nonn,base,hard

Author

Paolo P. Lava, Apr 10 2017

Extensions

a(11)-a(15) from Giovanni Resta, Apr 10 2017

a(16)-a(50) from Max Alekseyev, Nov 10 2022

Status

approved