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A186438
Positive numbers whose squares end in two identical digits.
5
10, 12, 20, 30, 38, 40, 50, 60, 62, 70, 80, 88, 90, 100, 110, 112, 120, 130, 138, 140, 150, 160, 162, 170, 180, 188, 190, 200, 210, 212, 220, 230, 238, 240, 250, 260, 262, 270, 280, 288, 290, 300, 310, 312, 320, 330, 338, 340, 350, 360, 362, 370, 380, 388, 390, 400, 410, 412
OFFSET
1,1
COMMENTS
The numbers are of the form : 10k, or 50k - 12, or 50k + 12, or 50k + 38.
REFERENCES
Jean Meeus, Letter to N. J. A. Sloane, Dec 26 1974.
LINKS
J. Meeus & N. J. A. Sloane, Correspondence, 1974-1975
Ana Rechtman, Juillet 2021, 4e défi, Images des Mathématiques, CNRS, 2021 (in French).
FORMULA
G.f.: 2*x*(5*x^6+x^5+4*x^4+5*x^3+4*x^2+x+5)/((x-1)^2 * (x^6+x^5+x^4+x^3+x^2+x+1)). [Colin Barker, Jul 02 2012]
EXAMPLE
62 is in the sequence because 62^2 = 3844.
MAPLE
with(numtheory):T:=array(1..10):for p from 1 to 1000 do:n:=p^2:l:=length(n):n0:=n:for
m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :T[m]:=u:od:if T[1]=T[2]
then printf(`%d, `, p):else fi:od:
MATHEMATICA
tidQ[n_]:=Module[{idn=IntegerDigits[n^2]}, idn[[-1]]==idn[[-2]]]; Select[ Range[ 4, 500], tidQ] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {10, 12, 20, 30, 38, 40, 50, 60}, 60] (* Harvey P. Dale, Jan 25 2014 *)
CROSSREFS
Cf. A016742 (even squares).
Sequence in context: A358998 A085772 A162189 * A346678 A035284 A265403
KEYWORD
nonn,base,easy
AUTHOR
Michel Lagneau, Feb 21 2011
STATUS
approved