This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A151972 #25 Sep 08 2022 08:45:38
%S A151972 0,1,6,10,15,16,21,25,30,31,36,40,45,46,51,55,60,61,66,70,75,76,81,85,
%T A151972 90,91,96,100,105,106,111,115,120,121,126,130,135,136,141,145,150,151,
%U A151972 156,160,165,166,171,175,180,181,186,190,195,196,201,205,210,211,216,220,225
%N A151972 Numbers that are congruent to {0, 1, 6, 10} mod 15.
%C A151972 Also, numbers n such that n^2 - n is divisible by 15.
%C A151972 Also, numbers n such that n^2 - n is divisible by 30.
%H A151972 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A151972 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
%F A151972 From _Wesley Ivan Hurt_, Jun 07 2016: (Start)
%F A151972 a(n) = (30*n-41-5*i^(2*n)+(3+3*i)*i^(-n)+(3-3*i)*i^n)/8 where i=sqrt(-1).
%F A151972 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. (End)
%F A151972 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
%p A151972 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
%t A151972 Select[Range[0, 300], Divisible[#^2-#, 15]&] (* _Harvey P. Dale_, Apr 01 2011, altered by _Eric M. Schmidt_, Aug 05 2012 *)
%o A151972 (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
%o A151972 (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
%Y A151972 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.
%Y A151972 Cf. A215202.
%K A151972 nonn,easy
%O A151972 1,3
%A A151972 _N. J. A. Sloane_, Aug 23 2009
%E A151972 This is a merge of two identical sequences, A151972 and A151975.