A363792 -id:A363792 - 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);

A363791 Starts of runs of 3 consecutive integers that are primitive binary Niven numbers (A363787).

Original entry on oeis.org

4184046, 5234670, 6285294, 7861230, 8123886, 8255214, 8255215, 8320878, 8353710, 8370126, 8379247, 12238830, 12451631, 12572622, 13623246, 13629935, 14515182, 14646510, 14673870, 14673871, 14679342, 15040494, 15335375, 15449071, 15531759, 15708078, 15986543, 16178670

Offset: 1

Amiram Eldar, Jun 22 2023

			4184046 is a term since 4184046, 4184047 and 4184048 are all primitive binary Niven numbers.

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

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

A363792 is a subsequence.

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++); }

cp's OEIS Frontend

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

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