A363792 Starts of runs of 4 consecutive integers that are primitive binary Niven numbers (A363787).

8255214, 14673870, 29092590, 33185646, 41743854, 47697390, 48069486, 56348622, 56999790, 58116078, 59604462, 60534702, 60813774, 61837038, 62581230, 64069614, 64999854, 65371950, 66581262, 66674286, 75232494, 83418606, 86767470, 88069806, 92255886, 95418702, 96441966, 99511758, 99604782

Offset

1,1

Comments

There are no runs of 5 or more consecutive integers that are primitive binary Niven numbers (see the second comment in A330933).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

8255214 is a term since 8255214, 8255215, 8255216 and 8255217 are all primitive binary Niven numbers.

Mathematica

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]

Prog

(PARI) 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++); }

Crossrefs

Subsequence of A049445, A330931, A330932, A330933, A363787, A363790 and A363791.

Sequence in context: A116337 A234049 A233484 * A234383 A192630 A098809

Adjacent sequences: A363789 A363790 A363791 * A363793 A363794 A363795

Keyword

nonn,base

Author

Amiram Eldar, Jun 22 2023

Status

approved