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%I #18 Nov 12 2022 03:10:53
%S 1,10,0,1101,11311,340210,4620020,12040210,151651121,1135531101,0,
%T 894105331101,0,15379177511311,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N 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.
%F Conjecture: a(n) = 0 for all n >= 15. - _Max Alekseyev_, Nov 10 2022
%e a(7) = 4620020 because:
%e 4620020 mod 2 = 0, 4620020 mod 3 = 2, 4620020 mod 4 = 0,
%e 4620020 mod 5 = 0, 4620020 mod 6 = 2, 4620020 mod 7 = 6,
%e 4620020 mod 8 = 4.
%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 (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);
%K nonn,base,hard
%O 1,2
%A _Paolo P. Lava_, Apr 10 2017
%E a(11)-a(15) from _Giovanni Resta_, Apr 10 2017
%E a(16)-a(50) from _Max Alekseyev_, Nov 10 2022
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