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.
38143807 is a term since 38143807, 38143808 and 38143809 are all in A376616: 38143807/A000120(38143807) = 2934139, and 2934139/A000120(2934139) = 225703 are integers, 38143808/A000120(38143808) = 4767976, and 4767976/A000120(4767976) = 595997 are integers, and 38143809/A000120(38143809) = 4238201, and 4238201/A000120(4238201) = 385291 are integers.
q[k_] := q[k] = Module[{w = DigitCount[k, 2, 1]}, Divisible[k, w] && Divisible[k/w, DigitCount[k/w, 2, 1]]]; Select[Range[10^8], q[#] && q[#+1] && q[#+2] &]
is1(k) = {my(w = hammingweight(k)); !(k % w) && !((k/w) % hammingweight(k/w));}
lista(kmax) = {my(q1 = is1(1), q2 = is1(2), q3); for(k = 3, kmax, q3 = is1(k); if(q1 && q2 && q3, print1(k-2, ", ")); q1 = q2; q2 = q3);}
ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
f[1] = 1; f[n_] := If[n > 0, i = ind[n - 1]; If[EvenQ[i], i++]; i, i = ind[-n]; If[OddQ[i], i++]; i];
negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
negFibQ[n_] := Divisible[n, negaFibTermsNum[-n]];
nConsec = 3; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0;
k = nConsec+1; While[c < 55, If[And @@ neg, c++; AppendTo[seq, k - nConsec]];neg = Join[Rest[neg], {negFibQ[k]}]; k++]; seq
126866286 is a term since 126866286/A000120(126866286) = 7048127, 126866287/A000120(126866287) = 6677173 and 126866288/A000120(126866288) = 7929143 are all prime numbers.
binMoranQ[n_] := PrimeQ[n / DigitCount[n, 2, 1]]; bin = binMoranQ /@ Range[3]; seq = {}; Do[If[And @@ bin, AppendTo[seq, k - 3]]; bin = Join[Rest[bin], {binMoranQ[k]}], {k, 4, 2 * 10^8}]; seq
4184046 is a term since 4184046, 4184047 and 4184048 are all primitive binary Niven numbers.
binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; primBinNivQ[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]);
seq[kmax_] := Module[{tri = primBinNivQ /@ Range[3], s = {}, k = 4}, While[k < kmax, If[And @@ tri, AppendTo[s, k - 3]]; tri = Join[Rest[tri], {primBinNivQ[k]}]; k++]; s]; seq[10^7]
isbinniv(n) = !(n % hammingweight(n));
isprim(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));
lista(kmax) = {my(tri = vector(3, i, isprim(i)), k = 4); while(k < kmax, if(vecsum(tri) == 3, print1(k-3, ", ")); tri = concat(vecextract(tri, "^1"), isprim(k)); k++); }
8255214 is a term since 8255214, 8255215, 8255216 and 8255217 are all primitive binary Niven numbers.
binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; primBinNivQ[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]);
seq[kmax_] := Module[{quad = primBinNivQ /@ Range[4], s = {}, k = 5}, While[k < kmax, If[And @@ quad, AppendTo[s, k - 4]]; quad = Join[Rest[quad], {primBinNivQ[k]}]; k++]; s]; seq[3*10^7]
isbinniv(n) = !(n % hammingweight(n));
isprim(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));
lista(kmax) = {my(quad = vector(4, i, isprim(i)), k = 5); while(k < kmax, if(vecsum(quad) == 4, print1(k-4, ", ")); quad = concat(vecextract(quad, "^1"), isprim(k)); k++); }
1 is a term since 1, 2 and 3 are terms of A093705.
divQ[n_] := Divisible[n, DivisorSum[n, DigitCount[#, 2, 1] &]]; div = divQ /@ Range[3]; Reap[Do[If[And @@ div, Sow[k - 3]]; div = Join[Rest[div], {divQ[k]}], {k, 4, 10^7}]][[2, 1]]
negaBinWt[n_] := negaBinWt[n] = If[n == 0, 0, negaBinWt[Quotient[n - 1, -2]] + Mod[n, 2]]; negaBinNivenQ[n_] := Divisible[n, negaBinWt[-n]]; nConsec = 3; neg = negaBinNivenQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec+1; While[c < 50, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negaBinNivenQ[k]}]; k++]; seq
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