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

Author

Amiram Eldar, Jun 22 2023

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

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]

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++); }