A135251 Maximal number of zero digits in square of number with n digits not divisible by 10.

0, 1, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124

Offset

1,3

Links

Table of n, a(n) for n=1..64.

Formula

2*n-4 <= a(n) <= 2*n-2 since, if k is an n-digit number not divisible by 10, then k^2 has at most 2*n digits of which the first and last are nonzero; and for n >= 2, the square of the n-digit number 10^(n-1)+1 contains 2*n-4 zeros. It seems likely that a(n) = 2*n-4 for all n >= 4. - Pontus von Brömssen, Jun 09 2025

Mathematica

(*For a(7)*) mx = 0; 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; If[ile > mx, mx = ile]], {t, 1, Length[w]}], {m, 1, 9}], {n, 0, 9}], {s, 0, 9}], {p, 0, 9}], {r, 0, 9}], {q, 0, 9}], {b, 1, 9}]; mx

Crossrefs

Cf. A058992, A134843, A134844, A134845, A134846, A134847, A134848, A134849, A135215, A135217, A135219, A135252, A135253.

Sequence in context: A173472 A334905 A058992 * A051755 A092535 A215476

Adjacent sequences: A135248 A135249 A135250 * A135252 A135253 A135254

Keyword

base,nonn

Author

Artur Jasinski, Nov 24 2007

Extensions

a(8)-a(64) from Pontus von Brömssen, Jun 09 2025

Status

approved