A363791 -id:A363791 - cp's OEIS frontend

A363790 Numbers k such that k and k+1 are both primitive binary Niven numbers (A363787).

115, 155, 204, 284, 355, 395, 404, 555, 564, 595, 675, 804, 835, 846, 1075, 1124, 1164, 1182, 1266, 1315, 1434, 1555, 1604, 1686, 1795, 1938, 2075, 2124, 2195, 2244, 2315, 2324, 2358, 2435, 2595, 3084, 3204, 3282, 3366, 4124, 4195, 4206, 4235, 4244, 4364, 4458

Offset: 1

Amiram Eldar, Jun 22 2023

			115 is a term since 115 and 116 are both primitive binary Niven numbers.

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

Subsequence of A049445, A330931 and A363787.

Subsequences: A363791, A363792.

binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; q[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]); Select[Range[5000], q[#] && q[# + 1] &]

isbinniv(n) = !(n % hammingweight(n));
isprim(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));
is(n) = isprim(n) && isprim(n+1);

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

Original entry on oeis.org

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

Amiram Eldar, Jun 22 2023

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

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

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

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

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++); }

cp's OEIS Frontend

A363790 Numbers k such that k and k+1 are both primitive binary Niven numbers (A363787).

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