A249181 a(n) = A057137(n)^2 where A057137 = 0,1,12,123,...,123...90,...

0, 1, 144, 15129, 1522756, 152399025, 15241383936, 1524155677489, 152415765279684, 15241578750190521, 1524157875019052100, 152415787526596567801, 15241578753153483936144, 1524157875322755800955129, 152415787532374345526722756, 15241578753238669120562399025

Offset

0,3

Comments

A very common playful operation on pocket calculators is to type as many digits 123... as the display allows and then squaring it by pressing the "X" and then the "=" key. On basic pocket calculators this yields an overflow with the first digits of, e.g., a(8) displayed, viz "E 1524157.6".

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (100, 0, 0, 0, 0, 0, 0, 0, 0, 10000000001, -1000000000100, 0, 0, 0, 0, 0, 0, 0, 0, -10000000000, 1000000000000).

Formula

For n<10, a(n) = A014824(n)^2 = floor(10^(n+1)/81-n/9)^2.

a(n) ~ 1.524157875...*10^(2n-2).

Example

a(3) = 123^2 = 15129.
a(10) = 1234567890^2 = 1524157875019052100.

Prog

(PARI) print1(t=0); for(i=1, 19, t=t*10+i%10; print1(", "t*t))
(PARI) A249181(n)=(137174210*10^n\1111111111)^2
(Magma) [(137174210*10^n div 1111111111)^2: n in [0..20]]; // Vincenzo Librandi, Oct 23 2014

Crossrefs

Sequence in context: A230969 A252779 A238284 * A352511 A260861 A079658

Adjacent sequences: A249178 A249179 A249180 * A249182 A249183 A249184

Keyword

nonn,base

Author

M. F. Hasler, Oct 22 2014

Status

approved