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

Author

M. F. Hasler, Oct 22 2014

Keywords

• nonn
• base

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".

Examples

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

Links

• 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).

Programs

Magma

[(137174210*10^n div 1111111111)^2: n in [0..20]]; // Vincenzo Librandi, Oct 23 2014

PARI

print1(t=0);for(i=1,19,t=t*10+i%10;print1(","t*t))

PARI

A249181(n)=(137174210*10^n\1111111111)^2

Formula

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

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