A319599
Numbers k such that k mod (2, 3, 4, ... , i+1) = (d_i, d_i-1, ..., d_1), where d_1, d_2, ..., d_i are the digits of k, with MSD(k) = d_1 and LSD(k) = d_i.
Original entry on oeis.org
0, 1, 10, 20, 1101, 1121, 11311, 31101, 40210, 340210, 4620020, 5431101, 7211311, 12040210, 24120020, 151651121, 165631101, 1135531101, 8084220020, 9117311311, 894105331101
Offset: 0
a(11) = 5431101 because:
5431101 mod 2 = 1, 5431101 mod 3 = 0, 5431101 mod 4 = 1,
5431101 mod 5 = 1, 5431101 mod 6 = 3, 5431101 mod 7 = 4,
5431101 mod 8 = 5.
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P:=proc(q) local a,i,j,n,ok; print(0); print(1); for n from 1 to q do
for i from 0 to 1 do a:=10*n+i; ok:=1; for j from 1 to ilog10(a)+1 do
if (a mod 10)<>((10*n+i) mod (j+1)) then ok:=0; break; else
a:=trunc(a/10); fi; od; if ok=1 then print(10*n+i); break; fi;
od; od; end: P(10^12);
A284814
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.
Original entry on oeis.org
1, 0, 0, 0, 11311, 0, 1032327, 11121217, 101033565, 0, 10333633323, 0, 0, 11121314781937, 0
Offset: 1
a(11) = 10333633323 because:
10333633323 mod 2 = 1, 10333633323 mod 3 = 0, 10333633323 mod 4 = 3,
10333633323 mod 5 = 3, 10333633323 mod 6 = 3, 10333633323 mod 7 = 6,
10333633323 mod 8 = 3, 10333633323 mod 9 = 3, 10333633323 mod 10 = 3,
10333633323 mod 11 = 2, 10333633323 mod 12 = 3.
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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 ((ilog10(n)+2-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);
Showing 1-2 of 2 results.
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