OFFSET
1,2
COMMENTS
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
Subsequence of primes gives A045468. - Ray Chandler, Jul 29 2019
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
A. Feist, On the Density of Birthday Sets, The Pentagon, 60 (No. 1, Fall 2000), 31-35.
A. Feist, Maple source for birthday sets. [Broken link]
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
A093722(n) = (a(n)^2 - 1)/120.
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
EXAMPLE
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 + ...
MAPLE
for n from 1 to 409 do if (n^2 mod 30 =1) then print(n) fi od; # Gary Detlefs, Apr 17 2012
MATHEMATICA
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 *)
PROG
(PARI) {a(n+1) = (n\4*3 + n%4)*10 + (-1)^(n\2)} /* Michael Somos, Oct 17 2006 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Andrew R. Feist (andrewf(AT)math.duke.edu), Sep 06 2000
EXTENSIONS
Corrected by Henry Bottomley, Jan 31 2002
Offset corrected to 1 by Ray Chandler, Jul 29 2019
STATUS
approved