A363792 - OEIS

%I #6 Jun 24 2023 13:23:11

%S 8255214,14673870,29092590,33185646,41743854,47697390,48069486,

%T 56348622,56999790,58116078,59604462,60534702,60813774,61837038,

%U 62581230,64069614,64999854,65371950,66581262,66674286,75232494,83418606,86767470,88069806,92255886,95418702,96441966,99511758,99604782

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

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

%H Amiram Eldar, <a href="/A363792/b363792.txt">Table of n, a(n) for n = 1..10000</a>

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

%t binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; primBinNivQ[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]);

%t 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]

%o (PARI) isbinniv(n) = !(n % hammingweight(n));

%o isprim(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));

%o 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++); }

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

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Jun 22 2023