A328213 -id:A328213 - cp's OEIS frontend

A330713 Numbers k such that both k and k+1 are Zeckendorf-Niven numbers (A328208) and lazy-Fibonacci-Niven numbers (A328212).

1, 7475, 10205, 13740, 40754, 52479, 93044, 95984, 141911, 151487, 196416, 198255, 202824, 202895, 213920, 231552, 335535, 339744, 363320, 366876, 404719, 408680, 434259, 446480, 487710, 495159, 504440, 528408, 585599, 607410, 645560, 646575, 665567, 735020, 736280

Offset: 1

Amiram Eldar, Dec 27 2019

nonn

Can 3 consecutive numbers be both Zeckendorf-Niven numbers and lazy-Fibonacci-Niven numbers? Equivalently, are there numbers that are both in A328210 and A328214?

			7475 is a term since A007895(7475) = 5 and A112310(7475) = 13 and both 5 and 13 are divisors of 7475, and A007895(7476) = 6 and A112310(7476) = 12 and both 6 and 12 are divisors of 7476.

Amiram Eldar, Table of n, a(n) for n = 1..1000

Intersection of A328209 and A328213.

Cf. A328208, A328210, A328212, A328214, A330711.

A331821 Positive numbers k such that -k and -(k + 1) are both negabinary-Niven numbers (A331728).

Original entry on oeis.org

2, 3, 8, 9, 15, 24, 27, 32, 33, 39, 54, 55, 63, 77, 111, 114, 115, 123, 128, 129, 135, 144, 159, 174, 175, 203, 234, 235, 245, 255, 264, 294, 295, 329, 370, 371, 384, 413, 414, 415, 444, 447, 474, 475, 495, 504, 507, 512, 513, 519, 534, 535, 543, 580, 581, 624

Offset: 1

Amiram Eldar, Jan 27 2020

			8 is a term since both -8 and -(8 + 1) = -9 are negabinary-Niven numbers: A039724(-8) = 1000 and 1 + 0 + 0 + 0 = 1 is a divisor of 8, and A039724(-9) = 1011 and 1 + 0 + 1 + 1 = 3 is a divisor of 9.

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

Cf. A005352, A027615, A039724, A328209, A328213, A330927, A330931, A331086, A331089, A331728, A331819, A331820.

negaBinWt[n_] := negaBinWt[n] = If[n == 0, 0, negaBinWt[Quotient[n - 1, -2]] + Mod[n, 2]]; negaBinNivenQ[n_] := Divisible[n, negaBinWt[-n]]; c = 0; k = 1; s = {}; v = Table[-1, {2}]; While[c < 60, If[negaBinNivenQ[k], v = Join[Rest[v], {k}]; If[AllTrue[Differences[v], # == 1 &], c++; AppendTo[s, k - 1]]]; k++]; s

cp's OEIS Frontend

A330713 Numbers k such that both k and k+1 are Zeckendorf-Niven numbers (A328208) and lazy-Fibonacci-Niven numbers (A328212).

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