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

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

1,1

Comments

A077433(n) = number of separating zeros.

Links

Table of n, a(n) for n=1..35.

Formula

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

Example

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

Mathematica

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 *)

Crossrefs

Cf. A020338, A004216, A077430.

Sequence in context: A083511 A067894 A094620 * A118133 A345404 A225186

Adjacent sequences: A077428 A077429 A077430 * A077432 A077433 A077434

Keyword

nonn,base

Author

Reinhard Zumkeller, Nov 05 2002

Status

approved