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A057538
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Birthday set of order 5: numbers congruent to +-1 modulo 2, 3, 4 and 5.
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11
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1, 11, 19, 29, 31, 41, 49, 59, 61, 71, 79, 89, 91, 101, 109, 119, 121, 131, 139, 149, 151, 161, 169, 179, 181, 191, 199, 209, 211, 221, 229, 239, 241, 251, 259, 269, 271, 281, 289, 299, 301, 311, 319, 329, 331, 341, 349, 359, 361, 371, 379, 389, 391, 401, 409
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OFFSET
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1,2
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COMMENTS
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Also numbers congruent to +-1 or +-11 modulo 30 and numbers k where (k^2 - 1)/120 is an integer; all but the first two prime legs of Pythagorean triangles which also have prime hypotenuses appear within in this sequence (A048161). - Henry Bottomley, Jan 31 2002
Numbers k such that k^2 == 1 (mod 30). - Gary Detlefs, Apr 16 2012
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LINKS
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FORMULA
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G.f.: x * (1 + 10*x + 8*x^2 + 10*x^3 + x^4) / ((1 - x) * (1 - x^4)). a(-1 - n) = -a(n). - Michael Somos, Jan 21 2012
4*a(n) = 30*(n+1) - 45 + 5*(-1)^n + 6*(-1)^floor((n+1)/2). - R. J. Mathar, Jul 30 2019
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EXAMPLE
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229 is congruent to 1 (mod 2), 1 (mod 3), 1 (mod 4) and -1 (mod 5).
x+ 11*x^2 + 19*x^3 + 29*x^4 + 31*x^5 + 41*x^6 + 49*x^7 + 59*x^8 + 61*x^9 + ...
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MAPLE
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for n from 1 to 409 do if (n^2 mod 30 =1) then print(n) fi od; # Gary Detlefs, Apr 17 2012
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MATHEMATICA
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a057538[n_] := Block[{f},
f[x_] :=
If[Mod[x, #] == 1 || Mod[x, #] == # - 1, True, False] & /@
Range[2, 5];
Select[Range[n], DeleteDuplicates[f[#]] == {True} &]]; a057538[409] (* Michael De Vlieger, Dec 26 2014 *)
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PROG
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(PARI) {a(n+1) = (n\4*3 + n%4)*10 + (-1)^(n\2)} /* Michael Somos, Oct 17 2006 */
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Andrew R. Feist (andrewf(AT)math.duke.edu), Sep 06 2000
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EXTENSIONS
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STATUS
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approved
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