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.
isa := n -> irem(irem(binomial(2*n, n), n), 2) = 1: select(isa, [seq(1..507, 2)]); # Peter Luschny, Nov 30 2023
A367782Q[n_]:=OddQ[Mod[Binomial[2n,n],n]]; Select[Range[1000],A367782Q] (* Paolo Xausa, Dec 01 2023 *)
for(n=1,510,if(bitand(binomial(2*n,n)%n,1),print1(n,", ")));
from math import comb from itertools import count, islice def A367782_gen(startvalue=1): # generator of terms >= startvalue return filter(lambda n: (comb(n<<1,n)%n)&1, count(max(startvalue+(startvalue&1^1),1),2)) A367782_list = list(islice(A367782_gen(),30)) # Chai Wah Wu, Nov 30 2023
2 is a term since A000931(2) = 0 is divisible by 2. 27 is a term since A000931(27) = 351 = 13 * 27 is divisible by 27.
With[{m = 1500}, Position[LinearRecurrence[{0, 1, 1}, {0, 0, 1}, m]/Range[m], _?IntegerQ] // Flatten]
lista(kmax) = {my(p1 = 0, p2 = 0, p3 = 1, p4); print1("1, 2, "); for(k = 4, kmax, p4 = p1 + p2; if(!(p4 % k), print1(k, ", ")); p1 = p2; p2 = p3; p3 = p4);}
2 is a term since A002203(2) = 6 = 2 * 3 is divisible by 2. 6 is a term since A002203(6) = 198 = 6 * 33 is divisible by 6.
Select[Range[50000], Divisible[LucasL[#, 2], #] &]
lista(kmax) = {my(p1 = 2, p2 = 6, p3); print1("1, 2, "); for(k = 3, kmax, p3 = p1 + 2*p2; if(!(p3 % k), print1(k, ", ")); p1 = p2; p2 = p3);}
6 is a term since A000930(6) = 6 is divisible by 6. 12 is a term since A000930(12) = 60 = 5 * 12 is divisible by 12.
With[{m = 50000}, Position[LinearRecurrence[{1, 0, 1}, {1, 1, 2}, m]/Range[m], _?IntegerQ] // Flatten]
lista(kmax) = {my(nc1 = 1, nc2 = 1, nc3 = 2, nc4); print1("1, "); for(k = 4, kmax, nc4 = nc1 + nc3; if(!(nc4 % k), print1(k, ", ")); nc1 = nc2; nc2 = nc3; nc3 = nc4);}
3 is a term since A001850(3) = 63 = 3 * 21 is divisible by 3. 9 is a term since A001850(9) = 1462563 = 9 * 162507 is divisible by 9.
Select[Range[1000], Divisible[LegendreP[#, 3], #] &]
lista(kmax) = {my(cd0 = 1, cd1 = 3, cd2); print1("1, "); for(k = 2, kmax, cd2 = (3*(2*k-1)*cd1 - (k-1)*cd0)/k; if(!(cd2 % k), print1(k, ", ")); cd0 = cd1; cd1 = cd2);}
2 is a term since A001850(2) = 6 = 2 * 3 is divisible by 2. 6 is a term since A001850(6) = 1806 = 6 * 301 is divisible by 6.
seq[kmax_] := Module[{sc0 = 1, sc1 = 2, sc2, s = {1}}, Do[sc2 = ((6*k-3)*sc1 - (k-2)*sc0)/(k+1); If[Divisible[sc2, k], AppendTo[s, k]]; sc0 = sc1; sc1 = sc2, {k, 2, kmax}]; s]; seq[27000]
lista(kmax) = {my(sc0 = 1, sc1 = 2, sc2); print1(1, ", "); for(k = 2, kmax, sc2 = ((6*k-3)*sc1 - (k-2)*sc0)/(k+1); if(!(sc2 % k), print1(k, ", ")); sc0 = sc1; sc1 = sc2);}
1 is a term since A001003(1) = 2 is divisible by 1. 33 is a term since A001003(33) = 37836272668898230450209 = 33 * 1146553717239340316673 is divisible by 33.
seq[kmax_] := Module[{sc0 = 1, sc1 = 1, sc2, s = {1}}, Do[sc2 = ((6*k-3)*sc1 - (k-2)*sc0)/(k+1); If[Divisible[sc2, k], AppendTo[s, k]]; sc0 = sc1; sc1 = sc2, {k, 2, kmax}]; s]; seq[10^5]
lista(kmax) = {my(sc0 = 1, sc1 = 1, sc2); print1(1, ", "); for(k = 2, kmax, sc2 = ((6*k-3)*sc1 - (k-2)*sc0)/(k+1); if(!(sc2 % k), print1(k, ", ")); sc0 = sc1; sc1 = sc2);}
21 is a term since A002426(21) = 1105350729 = 21 * 52635749 is divisible by 21.
Select[Range[1000], Divisible[4^#*JacobiP[#, -# - 1/2, -# - 1/2, -1/2], #] &]
lista(kmax) = {my(ct0 = 1, ct1 = 1, ct2); print1("1, "); for(k = 2, kmax, ct2 = ((2*k-1)*ct1 + 3*(k-1)*ct0)/k; if(!(ct2 % k), print1(k, ", ")); ct0 = ct1; ct1 = ct2);}
seq[kmax_] := Module[{f0 = 1, f1 = 2, f2, s = {1}}, Do[f2 = ((7*k^2 - 7*k + 2)*f1 + 8*(k-1)^2*f0)/k^2; If[Divisible[f2, k], AppendTo[s, k]]; f0 = f1; f1 = f2, {k, 2, kmax}]; s]; seq[5000]
lista(kmax) = {my(f0 = 1, f1 = 2, f2); print1("1, "); for(k = 2, kmax, f2 = ((7*k^2 - 7*k + 2)*f1 + 8*(k-1)^2*f0)/k^2; if(!(f2 % k), print1(k, ", ")); f0 = f1; f1 = f2);}
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