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%I #8 Apr 10 2017 12:34:33
%S 1,0,0,0,11311,0,1032327,11121217,101033565,0,10333633323,0,0,
%T 11121314781937,0
%N 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.
%C Suggested by Francis Maleval in Linkedin "Number Theory" group.
%e a(11) = 10333633323 because:
%e 10333633323 mod 2 = 1, 10333633323 mod 3 = 0, 10333633323 mod 4 = 3,
%e 10333633323 mod 5 = 3, 10333633323 mod 6 = 3, 10333633323 mod 7 = 6,
%e 10333633323 mod 8 = 3, 10333633323 mod 9 = 3, 10333633323 mod 10 = 3,
%e 10333633323 mod 11 = 2, 10333633323 mod 12 = 3.
%p 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
%p ok:=1; a:=n; for j from 1 to ilog10(n)+1 do if (a mod 10)<>n mod ((ilog10(n)+2-j)+1)
%p then ok:=0; break; else a:=trunc(a/10); fi; od; if ok=1 then print(n); d:=1; break; fi; od;
%p if n=10^k and d=0 then print(0); fi; od; end: P(20);
%Y Cf. A284815.
%K nonn,base,hard,more
%O 1,5
%A _Paolo P. Lava_, Apr 10 2017
%E a(12)-a(15) from _Giovanni Resta_, Apr 10 2017
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