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A284815
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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.
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2
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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Conjecture: a(n) = 0 for all n >= 15. - Max Alekseyev, Nov 10 2022
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn,base,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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