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 A151972 Numbers that are congruent to {0, 1, 6, 10} mod 15. 3
 0, 1, 6, 10, 15, 16, 21, 25, 30, 31, 36, 40, 45, 46, 51, 55, 60, 61, 66, 70, 75, 76, 81, 85, 90, 91, 96, 100, 105, 106, 111, 115, 120, 121, 126, 130, 135, 136, 141, 145, 150, 151, 156, 160, 165, 166, 171, 175, 180, 181, 186, 190, 195, 196, 201, 205, 210, 211, 216, 220, 225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also, numbers n such that n^2 - n is divisible by 15. Also, numbers n such that n^2 - n is divisible by 30. LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA G.f.: x^2*(1+5*x+4*x^2+5*x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011 From Wesley Ivan Hurt, Jun 07 2016: (Start) a(n) = (30*n-41-5*i^(2*n)+(3+3*i)*i^(-n)+(3-3*i)*i^n)/8 where i=sqrt(-1). a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. (End) E.g.f.: (20 + (15*x - 23)*cosh(x) + 3*(sin(x) + cos(x) + (5*x - 6)*sinh(x)))/4. - Ilya Gutkovskiy, Jun 07 2016 MAPLE A151972:=n->(30*n-41-5*I^(2*n)+(3+3*I)*I^(-n)+(3-3*I)*I^n)/8: seq(A151972(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016 MATHEMATICA Select[Range[0, 300], Divisible[#^2-#, 15]&]  (* Harvey P. Dale, Apr 01 2011, altered by Eric M. Schmidt, Aug 05 2012 *) PROG (MAGMA) [ n : n in [0..1000] | n mod 15 in [0, 1, 6, 10]]; // Vincenzo Librandi, Apr 02 2011, simplified by Eric M. Schmidt, Aug 05 2012 (MAGMA) [ n: n in [0..1000] | (n^2-n) mod (15) eq 0 ]; // Vincenzo Librandi, Apr 03 2011, altered by Eric M. Schmidt, Aug 05 2012 CROSSREFS For m^2 == m (mod n), see: n=2: A001477, n=3: A032766, n=4: A042948, n=5: A008851, n=6: A032766, n=7: A047274, n=8: A047393, n=9: A090570, n=10: A008851, n=11: A112651, n=12: A112652, n=13: A112653, n=14: A047274, n=15: A151972, n=16: A151977, n=17: A151978, n=18: A090570, n=19: A151979, n=20: A151980, n=21: A151971, n=22, A112651, n=24: A151973, n=26: A112653, n=30: A151972, n=32: A151983, n=34: A151978, n=38: A151979, n=42: A151971, n=48: A151981, n=64: A151984. Cf. A215202. Sequence in context: A074980 A059218 A095678 * A094564 A271354 A315240 Adjacent sequences:  A151969 A151970 A151971 * A151973 A151974 A151975 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Aug 23 2009 EXTENSIONS This is a merge of two identical sequences, A151972 and A151975. STATUS approved

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Last modified May 27 18:56 EDT 2020. Contains 334664 sequences. (Running on oeis4.)