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

Author

Paolo P. Lava, Apr 10 2017

Keywords

• nonn
• base
• hard

Examples

			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.
		

Programs

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);

Formula

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

Extensions

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

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