A135216 - OEIS

%I #5 Nov 07 2013 04:24:55

%S 18,3,13,1,7,1

%N a(n)= number of numbers with n+1 digits and without zero digits whose squares have maximal number of zero digits = A135215(n+1).

%e a(1)=18 because we have 18 numbers with 2 digits and without zero digit whose square have maximal possible value 1 zero: 32, 33, 45, 47, 48, 49, 51, 52, 53, 55, 64, 71, 78, 84, 95, 97, 98, 99.

%e a(2)=3 because we have 3 numbers with 3 digits and without zero digit whose square have maximal possible value 3 zeros: 448, 548, 949.

%e a(3)=13 because we have 13 numbers with 4 digits and without zero digit whose square have maximal possible value 4 zeros: 3747, 3751, 4899, 6245, 6249, 6253, 7746, 7747, 7749, 7751, 7753, 9747, 9798.

%e a(4)=1 because we have only one number with 5 digits and without zero digit whose square have maximal possible value 6 zeros: 62498.

%e a(5)=7 because we have 7 numbers with 6 digits and without zero digit whose square have maximal possible value 7 zeros: 248998, 316245, 489898, 498999, 781249, 948951, 997998.

%e a(6)=1 because we have only one number with 7 digits and without zero digit whose square have maximal possible value 10 zeros: 6244998.

%t (*For a(7) *) c = 0; mx = 10; Do[Do[Do[Do[Do[Do[Do[k = 10^6b + 10^5q + 10^4r + 10^3p + 10^2s + 10n + m; w = IntegerDigits[k^2]; ile = 0; Do[If[w[[t]] == 0, ile = ile + 1], {t, 1, Length[w]}]; If[ile == mx, c = c + 1], {m, 1, 9}], {n, 1, 9}], {s, 1, 9}], {p, 1, 9}], {r, 1, 9}], {q, 1, 9}], {b, 1, 9}]; c (*Artur Jasinski*)

%Y Cf. A134843, A134844, A134845, A134846, A134847, A134848, A134849, A135215, A135217, A135219.

%K nonn,base

%O 1,1

%A _Artur Jasinski_, Nov 23 2007