

A106497


Numbers whose square is the concatenation of two identical numbers, i.e., of the form NN.


47



36363636364, 45454545455, 54545454546, 63636363637, 72727272728, 81818181819, 90909090910, 428571428571428571429, 571428571428571428572, 714285714285714285715, 857142857142857142858
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OFFSET

1,1


COMMENTS

For the corresponding numbers N see A102567.
Numbers of the form j*(10^d + 1)/k where 10^d + 1 == 0 (mod k^2) and k/sqrt(10) < j < k.  David W. Wilson, Nov 09 2006


REFERENCES

R. Ondrejka, Problem 1130: Biperiod Squares, Journal of Recreational Mathematics, Vol. 14:4 (198182), 299. Solution by F. H. Kierstead, Jr., JRM, Vol. 15:4 (198283), 311312.


LINKS

David W. Wilson, Table of n, a(n) for n = 1..1098


EXAMPLE

63636363637 is in the sequence because 63636363637^2 = 4049586776940495867769 is 40495867769 written twice.


CROSSREFS

Cf. A092118, A102567.
Sequence in context: A022262 A233849 A116279 * A204097 A295355 A178221
Adjacent sequences: A106494 A106495 A106496 * A106498 A106499 A106500


KEYWORD

base,nonn


AUTHOR

Lekraj Beedassy, May 04 2005


EXTENSIONS

a(7) from Klaus Brockhaus, May 06 2005
More terms from David W. Wilson, Nov 05 2006
Reference and crossreferences added by William Rex Marshall, Nov 12 2010


STATUS

approved



