A352090 -id:A352090 - cp's OEIS frontend

A364124 Numbers k such that k and k+1 are both Stolarsky-Niven numbers (A364123).

8, 56, 84, 159, 195, 224, 384, 399, 405, 995, 1140, 1224, 1245, 1295, 1309, 1419, 1420, 1455, 1474, 1507, 2585, 2597, 2600, 2680, 2681, 2727, 2744, 2750, 2799, 2855, 3122, 3311, 3339, 3345, 3618, 3707, 3795, 4004, 6770, 6774, 6984, 6985, 7014, 7074, 7154, 7405

Offset: 1

Amiram Eldar, Jul 07 2023

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

Subsequence of A364123.
Subsequences: A364125, A364126.
Similar sequences: A330927, A328205, A328209, A328213, A330931, A331086, A333427, A334309, A331820, A342427, A344342, A351715, A351720, A352090, A352108, A352321, A352343, A352509.

seq[count_, nConsec_] := Module[{cn = stolNivQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ cn, c++; AppendTo[s, k - nConsec]]; cn = Join[Rest[cn], {stolNivQ[k]}]; k++]; s]; seq[50, 2] (* using the function stolNivQ[n] from A364123 *)

lista(count, nConsec) = {my(cn = vector(nConsec, i, isStolNivQ(i)), c = 0, k = nConsec + 1); while(c < count, if(vecsum(cn) == nConsec, c++; print1(k-nConsec, ", ")); cn = concat(vecextract(cn, "^1"), isStolNivQ(k)); k++);} \\ using the function isA364123(n) from A364123
lista(50, 2)

A376029 Tribonacci-Niven numbers (A352089) with a record gap to the next tribonacci-Niven number.

Original entry on oeis.org

1, 2, 8, 48, 140, 244, 620, 705, 1395, 6210, 9656, 14322, 52024, 88128, 95589, 119440, 151130, 325105, 407128, 472790, 520971, 686103, 4456608, 7066416, 13207389, 15488160, 23381160, 42317212, 49496700, 53564016, 128163495, 165750096, 387900480, 421730960, 485880806

Offset: 1

Amiram Eldar, Sep 06 2024

The corresponding record gaps are 1, 2, 4, 8, 9, 12, 15, 20, ... (see the link for more values).

Ray (2005) and Ray and Cooper (2006) proved that the asymptotic density of the tribonacci-Niven numbers is 0. Therefore, this sequence is infinite.

			The first 7 tribonacci-Niven numbers are 1, 2, 4, 6, 7, 8 and 12. The gaps between them are 1, 2, 2, 1, 1 and 4, and the record gaps, 1, 2 and 4 occur after 1, 2 and 8, the first 3 terms of this sequence.

Andrew B. Ray, On the natural density of the k-Zeckendorf Niven numbers, Ph.D. dissertation, Central Missouri State University, 2005.

Amiram Eldar, Table of n, a(n) for n = 1..42
Amiram Eldar, Table of n, a(n), gap(n) for n = 1..42
Andrew Ray and Curtis Cooper, On the natural density of the k-Zeckendorf Niven numbers, J. Inst. Math. Comput. Sci. Math., Vol. 19 (2006), pp. 83-98.

Cf. A352089, A352090.

Similar sequences: A337076, A337077, A347495, A347496, A376028.

t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; tnQ[n_] := Module[{s = 0, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; s++; m -= t[k]; k = 1]; Divisible[n, s]]; seq[kmax_] := Module[{gapmax = 0, gap, k1 = 1, s = {}}, Do[If[tnQ[k], gap = k - k1; If[gap > gapmax, gapmax = gap; AppendTo[s, k1]]; k1 = k], {k, 2, kmax}]; s]; seq[10^4]

cp's OEIS Frontend

A364124 Numbers k such that k and k+1 are both Stolarsky-Niven numbers (A364123).

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