A077433 -id:A077433 - cp's OEIS frontend

A077430 a(n) = floor(log_10(2*n^2)) + 1.

1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Reinhard Zumkeller, Nov 05 2002

nonn

Cf. A077431, A077432, A004216, A077429, A077433.

A077431 n repeated in decimal representation, but separated by enough zeros that the square has the pattern (n^2)(2n^2)(n^2).

Original entry on oeis.org

11, 22, 303, 404, 505, 606, 707, 8008, 9009, 10010, 11011, 12012, 13013, 14014, 15015, 16016, 17017, 18018, 19019, 20020, 21021, 22022, 230023, 240024, 250025, 260026, 270027, 280028, 290029, 300030, 310031, 320032, 330033, 340034, 350035

Offset: 1

Reinhard Zumkeller, Nov 05 2002

A077433(n) = number of separating zeros.

			a(17) = 17017, as 17017^2 = 289578289 = A077432(17) = 289'578'289 and 289=17^2 and 578=2*289.

Cf. A020338, A004216, A077430.

a[n_] := For[idn = IntegerDigits[n]; k = 0, True, k++, an = FromDigits[ Join[idn, Table[0, k], idn]]; If[MatchQ[IntegerDigits[an^2], {b__ /; IntegerQ[Sqrt[FromDigits[{b}]]], c___, 0..., b__} /; FromDigits[{c}] == 2*FromDigits[{b}]], Return[an]]];
Array[a, 35] (* Jean-François Alcover, Nov 13 2017 *)

a(n) = n*(1+10^(1+floor(log_10(2*n^2)))).

cp's OEIS Frontend

A077430 a(n) = floor(log_10(2*n^2)) + 1.

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A077431 n repeated in decimal representation, but separated by enough zeros that the square has the pattern (n^2)(2n^2)(n^2).

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