A334345 -id:A334345 - cp's OEIS frontend

A334346 Starts of runs of 3 consecutive binary Moran numbers (A334344).

126866286, 133542126, 148891086, 150959502, 173668302, 207567342, 227950542, 257154606, 263874222, 284421582, 295075566, 331190766, 373024206, 390589326, 392805486, 393817806, 395760366, 397921806, 441314766, 459700686, 459990702, 516188142, 527006286, 586869966

Offset: 1

Amiram Eldar, Apr 23 2020

			126866286 is a term since 126866286/A000120(126866286) = 7048127, 126866287/A000120(126866287) = 6677173 and 126866288/A000120(126866288) = 7929143 are all prime numbers.

Amiram Eldar, Table of n, a(n) for n = 1..3410 (terms below 10^11)

Subsequence of A330932, A334344 and A334345.

Cf. A000120, A235397.

binMoranQ[n_] := PrimeQ[n / DigitCount[n, 2, 1]]; bin = binMoranQ /@ Range[3]; seq = {}; Do[If[And @@ bin, AppendTo[seq, k - 3]]; bin = Join[Rest[bin], {binMoranQ[k]}], {k, 4, 2 * 10^8}]; seq

A338514 Numbers k such that k and k+1 are both divisible by the total binary weight of their divisors (A093653).

Original entry on oeis.org

1, 2, 54, 2119, 11100, 13727, 14382, 15799, 16399, 20159, 20950, 33421, 34617, 36328, 36396, 39400, 42198, 42438, 42650, 46253, 46873, 50370, 55368, 56600, 58793, 67013, 67320, 69023, 72325, 76057, 86393, 90781, 92906, 93216, 105909, 132088, 134028, 134823, 140466

Offset: 1

Amiram Eldar, Oct 31 2020

Numbers k such that k and k+1 are both in A093705, or, equivalently, k is divisible by A093653(k) and k+1 is divisible by A093653(k+1).

			1 is a term since 1 and 2 are both terms of A093705.

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

Cf. A000120, A093653, A093705.

Similar sequences: A330927, A330931, A334345, A338452.

divQ[n_] := Divisible[n, DivisorSum[n, DigitCount[#, 2, 1] &]]; q1 = divQ[1]; Reap[Do[q2 = divQ[n]; If[q1 && q2, Sow[n - 1]]; q1 = q2, {n, 2, 10^5}]][[2, 1]]
SequencePosition[Table[If[Divisible[n,Total[DigitCount[Divisors[n],2,1]]],1,0],{n,150000}],{1,1}][[All,1]] (* Harvey P. Dale, Jun 14 2022 *)

cp's OEIS Frontend

A334346 Starts of runs of 3 consecutive binary Moran numbers (A334344).

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