A085944 - OEIS

A085944

Let S = 12345678901234567890123456..., the cyclic concatenation of digits; partition this string into distinct squarefree numbers. To avoid leading zeros, no member may end with the digit 9.

%I #10 Sep 24 2023 04:30:30

%S 1,2,3,4567,890,123,45678,901,23,4567890,1234,5,6,7,89012345,67,

%T 89012345678,90123,45678901,2345,678,901234,5678,9012345,67890,12345,

%U 678901,2345678,901234567,8901234567890,1234567,8901234567890123

%N Let S = 12345678901234567890123456..., the cyclic concatenation of digits; partition this string into distinct squarefree numbers. To avoid leading zeros, no member may end with the digit 9.

%e a(4) = 4567 because 4567 is squarefree, while 4, 45 and 456 are not.

%e a(5) = 890 because 89 would cause a(6) to have a leading 0.

%o (PARI) used = matrix(9, 60); x = 1; for (n = 1, 80, num = x; s = x; d = 1; while (used[s, d] || !issquarefree(num) || x == 9, x = (x + 1)%10; num = 10*num + x; d++); print1(num, ", "); used[s, d] = 1; x++); \\ _David Wasserman_, Feb 14 2005

%Y Cf. A085943.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Jul 14 2003

%E Corrected and extended by _David Wasserman_, Feb 14 2005