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A249181
a(n) = A057137(n)^2 where A057137 = 0,1,12,123,...,123...90,...
1
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
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Oct 22 2014
STATUS
approved