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A008851
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Congruent to 0 or 1 mod 5.
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37
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0, 1, 5, 6, 10, 11, 15, 16, 20, 21, 25, 26, 30, 31, 35, 36, 40, 41, 45, 46, 50, 51, 55, 56, 60, 61, 65, 66, 70, 71, 75, 76, 80, 81, 85, 86, 90, 91, 95, 96, 100, 101, 105, 106, 110, 111, 115, 116, 120, 121, 125, 126, 130, 131, 135, 136, 140, 141, 145, 146, 150, 151
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OFFSET
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1,3
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COMMENTS
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Numbers k that have the same last digit as k^2.
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REFERENCES
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L. E. Dickson, History of the Theory of Numbers, I, p. 459.
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LINKS
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FORMULA
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G.f.: x^2*(1+4*x) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 07 2011
E.g.f.: 4 + ((10*x - 13)*exp(x) - 3*exp(-x))/4. - David Lovler, Sep 11 2022
Sum_{n>=2} (-1)^n/a(n) = sqrt(1+2/sqrt(5))*Pi/10 + log(phi)/(2*sqrt(5)) + log(5)/4, where phi is the golden ratio (A001622). - Amiram Eldar, Oct 12 2022
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+5 od: seq(a[n], n=0..61); # Zerinvary Lajos, Mar 16 2008
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MATHEMATICA
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Select[Range[0, 151], MemberQ[{0, 1}, Mod[#, 5]] &] (* T. D. Noe, Mar 31 2013 *)
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PROG
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(Haskell)
a008851 n = a008851_list !! (n-1)
a008851_list = [10*n + m | n <- [0..], m <- [0, 1, 5, 6]]
(PARI) a(n) = 5*(n\2)+bitand(n, 1); /* Joerg Arndt, Mar 31 2013 */
(PARI) a(n) = floor((5/3)*floor(3*(n-1)/2)); /* Joerg Arndt, Mar 31 2013 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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