A154701 -id:A154701 - cp's OEIS frontend

A352344 Starts of runs of 3 consecutive lazy-Pell-Niven numbers (A352342).

2196, 2650, 5784, 17459, 28950, 57134, 112878, 124506, 147078, 162809, 169694, 191538, 210494, 218654, 223344, 223459, 230894, 239360, 258740, 277455, 278900, 285615, 289695, 291328, 291858, 295408, 311524, 314658, 324734, 332894, 335179, 341900, 347718, 362880

Offset: 1

Amiram Eldar, Mar 12 2022

			2196 is a term since 2196, 2197 and 2198 are all divisible by the sum of the digits in their maximal Pell representation:
     k  A352339(k)  A352340(k)  k/A352340(k)
  ----  ----------  ----------  ------------
  2196   121222020          12           183
  2197   121222021          13           169
  2198   121222022          14           157

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

Cf. A352339, A352340.
Subsequence of A352342 and A352343.
A352345 is a subsequence.
Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322.

pell[1] = 1; pell[2] = 2; pell[n_] := pell[n] = 2*pell[n - 1] + pell[n - 2]; pellp[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[pell[k] <= m, k++]; k--; AppendTo[s, k]; m -= pell[k]; k = 1]; IntegerDigits[Total[3^(s - 1)], 3]]; lazyPellNivenQ[n_] := Module[{v = pellp[n]}, nv = Length[v]; i = 1; While[i <= nv - 2, If[v[[i]] > 0 && v[[i + 1]] == 0 && v[[i + 2]] < 2, v[[i ;; i + 2]] += {-1, 2, 1}; If[i > 2, i -= 3]]; i++]; i = Position[v, ?(# > 0 &)]; Divisible[n, Plus @@ v[[i[[1, 1]] ;; -1]]]]; seq[count, nConsec_] := Module[{lpn = lazyPellNivenQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ lpn, c++; AppendTo[s, k - nConsec]]; lpn = Join[Rest[lpn], {lazyPellNivenQ[k]}]; k++]; s]; seq[30, 3]

A352510 Starts of runs of 3 consecutive Catalan-Niven numbers (A352508).

Original entry on oeis.org

4, 55, 144, 145, 511, 2943, 6950, 7734, 9470, 9750, 15630, 15631, 35034, 35464, 41590, 41986, 64735, 68523, 68870, 77510, 81150, 90958, 106063, 118264, 119043, 135970, 139403, 163188, 164862, 164863, 171346, 181510, 200759, 202761, 202762, 208024, 209230, 209586

Offset: 1

Amiram Eldar, Mar 19 2022

			4 is a term since 4, 5 and 6 are all Catalan-Niven numbers: the Catalan representation of 4, A014418(20) = 20, has the sum of digits 2+0 = 2 and 4 is divisible by 2, the Catalan representation of 5, A014418(5) = 100, has the sum of digits 1+0+0 = 1 and 5 is divisible by 1, and the Catalan representation of 6, A014418(6) = 101, has the sum of digits 1+0+1 = 2 and 6 is divisible by 2.

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

Cf. A000108, A014418, A014420.
Subsequence of A352508 and A352509.
A352511 is a subsequence.
Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322, A352344.

c[n_] := c[n] = CatalanNumber[n]; catNivQ[n_] := Module[{s = {}, m = n, i}, While[m > 0, i = 1; While[c[i] <= m, i++]; i--; m -= c[i]; AppendTo[s, i]]; Divisible[n, Plus @@ IntegerDigits[Total[4^(s - 1)], 4]]]; seq[count_, nConsec_] := Module[{cn = catNivQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ cn, c++; AppendTo[s, k - nConsec]]; cn = Join[Rest[cn], {catNivQ[k]}]; k++]; s]; seq[30, 3]

A364218 Starts of runs of 3 consecutive integers that are Jacobsthal-Niven numbers (A364216).

Original entry on oeis.org

1, 2, 14, 42, 43, 44, 86, 182, 544, 686, 846, 854, 1014, 1375, 1384, 1504, 1624, 2105, 2190, 2315, 2358, 2731, 2732, 2763, 2774, 2824, 3243, 3534, 3702, 4205, 4878, 5046, 5408, 5462, 5643, 5663, 6222, 6390, 6935, 7566, 7734, 7928, 8224, 8704, 8910, 9078, 9368

Offset: 1

Amiram Eldar, Jul 14 2023

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

Subsequence of A364216 and A364217.
Subsequence of A364219, A364220, A364221.
Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322, A352344, A352510.

consecJacobsthalNiven[10^4, 3] (* using the function from A364217 *)

lista(10^4, 3) \\ using the function from A364217

A364381 Starts of runs of 3 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).

Original entry on oeis.org

1, 2, 3, 4, 8, 9, 10, 14, 20, 26, 42, 43, 44, 84, 85, 86, 104, 115, 170, 182, 304, 344, 362, 414, 544, 682, 686, 692, 784, 854, 1014, 1370, 1384, 1504, 1673, 1685, 1706, 2224, 2315, 2358, 2730, 2731, 2732, 2763, 2774, 3243, 3594, 3702, 4144, 4688, 4864, 5046, 5408

Offset: 1

Amiram Eldar, Jul 21 2023

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

Cf. A265745, A265747.
Subsequence of A364379 and A364380.
Subsequences: A364382, A364383.
Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322, A352344, A352510, A364218.

consecGreedyJN[5500, 3] (* using the function consecGreedyJN from A364380 *)

lista(5500, 3) \\ using the function lista from A364380

A381583 Starts of runs of 3 consecutive integers that are all terms in A381581.

Original entry on oeis.org

1, 2, 20, 55, 56, 110, 304, 364, 398, 846, 1024, 1084, 1744, 1854, 2044, 2104, 2105, 2527, 2824, 2862, 3870, 4374, 5222, 5223, 5243, 5718, 5928, 6488, 6784, 6844, 6894, 6978, 7142, 7924, 10590, 11240, 11889, 11975, 12248, 14284, 14915, 16638, 17710, 17714, 17824

Offset: 1

Amiram Eldar, Feb 28 2025

If k is congruent to 1 or 5 mod 12 (A087445), then A001906(k) = Fibonacci(2*k) is a term.

			1 is a term since A291711(1) = 1 divides 1, A291711(2) = 2 divides 2, and A291711(3) = 1 divides 3.
20 is a term since A291711(20) = 4 divides 20, A291711(21) = 1 divides 21, and A291711(22) = 2 divides 22.

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

Cf. A000045, A001906, A087445, A291711.
Subsequence of A381581 and A381582.
Subsequences: A381584, A381585.
Similar sequences: A154701, A328210, A330932, A351721.

f[n_] := f[n] = Fibonacci[2*n]; q[n_] := q[n] = Module[{s = 0, m = n, k}, While[m > 0, k = 1; While[m > f[k], k++]; If[m < f[k], k--]; If[m >= 2*f[k], s += 2; m -= 2*f[k], s++; m -= f[k]]]; Divisible[n, s]]; seq[count_, nConsec_] := Module[{cn = q /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ cn, c++; AppendTo[s, k - nConsec]]; cn = Join[Rest[cn], {q[k]}]; k++]; s]; seq[45, 3]

mx = 20; fvec = vector(mx, i, fibonacci(2*i)); f(n) = if(n <= mx, fvec[n], fibonacci(2*n));
is1(n) = {my(s = 0, m = n, k); while(m > 0, k = 1; while(m > f(k), k++); if(m < f(k), k--); if(m >= 2*f(k), s += 2; m -= 2*f(k), s++; m -= f(k))); !(n % s);}
list(lim) = {my(q1 = is1(1), q2 = is1(2), q3); for(k = 3, lim, q3 = is1(k); if(q1 && q2 && q3, print1(k-2, ", ")); q1 = q2; q2 = q3);}

A364008 Starts of runs of 3 consecutive integers that are Wythoff-Niven numbers (A364006).

Original entry on oeis.org

6, 54, 374, 375, 978, 979, 14695, 15694, 17708, 17709, 34990, 36476, 38374, 41699, 45304, 75944, 85149, 93104, 113463, 114560, 116170, 117754, 120274, 121371, 203983, 221804, 250118, 259819, 270214, 270477, 275526, 276912, 288125, 297241, 297515, 299824, 309440

Offset: 1

Amiram Eldar, Jul 01 2023

Amiram Eldar, Table of n, a(n) for n = 1..3000

Subsequence of A364006 and A364007.
A364009 is a subsequence.
Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322, A352510.

seq[10, 3] (* generates the first 10 terms using the function seq[count, nConsec] from A364007 *)

A364125 Starts of runs of 3 consecutive integers that are Stolarsky-Niven numbers (A364123).

Original entry on oeis.org

1419, 2680, 6984, 18765, 20383, 28390, 48697, 55560, 69056, 121913, 125340, 125341, 125739, 133614, 135189, 136409, 140789, 147563, 150138, 155518, 157068, 171819, 317933, 318188, 319395, 323685, 339723, 340846, 349326, 356290, 371041, 389010, 392903, 393809, 400608

Offset: 1

Amiram Eldar, Jul 07 2023

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

Subsequence of A364123 and A364124.
Subsequence: A364126.
Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322, A352344, A352510.

seq[10, 3] (* generates the first 10 terms, using the function seq[count, nConsec] from A364124 *)

lista(10, 3) \\ generates the first 10 terms, using the function lista(count, nConsec) from A364124

A331090 Positive numbers k such that -k, -(k + 1), and -(k + 2) are 3 consecutive negative negaFibonacci-Niven numbers (A331088).

Original entry on oeis.org

1, 2, 20, 54, 55, 56, 110, 376, 398, 974, 986, 1084, 1744, 2464, 2524, 3304, 3870, 5223, 5718, 6095, 6124, 6184, 6663, 6764, 6844, 7142, 7684, 9035, 9124, 10590, 11598, 11975, 12606, 13444, 13504, 14284, 14915, 17164, 17643, 17710, 17714, 17824, 17884, 18698, 18905, 19494, 23191, 24243, 24785, 25542, 26382, 27390, 29644, 34278, 35464

Offset: 1

Amiram Eldar, Jan 08 2020

Numbers of the form F(6*k + 2) - 1 and F(6*k + 4) - 1, where F(m) is the m-th Fibonacci number, are terms.

If m is of the form F(k) - 1, where k > 2 is congruent to {2, 10} mod 24, then {-m, -(m + 1), -(m + 2), -(m + 3), -(m + 4)} are 5 consecutive negative negaFibonacci-Niven numbers.

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

Cf. A000045, A154701, A269819, A328210, A328214, A330932, A331087, A331088.

ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
f[1] = 1; f[n_] := If[n > 0, i = ind[n - 1]; If[EvenQ[i], i++]; i, i = ind[-n]; If[OddQ[i], i++]; i];
negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
negFibQ[n_] := Divisible[n, negaFibTermsNum[-n]];
nConsec = 3; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0;
k = nConsec+1; While[c < 55, If[And @@ neg, c++; AppendTo[seq, k - nConsec]];neg = Join[Rest[neg], {negFibQ[k]}]; k++]; seq

A334371 Starts of runs of 3 consecutive Moran numbers (A001101).

Original entry on oeis.org

3031, 13116, 46824, 201614, 456325, 1310412, 1499434, 1825225, 2217620, 2318423, 2522540, 2784634, 3132380, 3276024, 3931226, 4013113, 4555476, 5017340, 5211380, 6309602, 6338910, 6526835, 7197154, 8678920, 9108023, 9258002, 10256420, 10533620, 10614266, 10810824

Offset: 1

Amiram Eldar, Apr 25 2020

			3031 is a term since 3031/(3+0+3+1) = 433, 3032/(3+0+3+2) = 379 and 3033/(3+0+3+3) = 337 are all primes.

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

Subsequence of A001101, A085775 and A154701.

Cf. A235397, A334346.

moranQ[n_] := PrimeQ[n / Plus @@ IntegerDigits[n]]; m = moranQ /@ Range[3]; seq = {}; Do[If[And @@ m, AppendTo[seq, k - 3]]; m = Join[Rest[m], {moranQ[k]}], {k, 4, 10^6}]; seq

A338515 Starts of runs of 3 consecutive numbers that are divisible by the total binary weight of their divisors (A093653).

Original entry on oeis.org

1, 348515, 8612344, 29638764, 30625110, 32039808, 32130600, 32481682, 43664313, 55318282, 55503719, 59671714, 69254000, 73152296, 93470904, 100366594, 103640097, 105026790, 109038462, 109212287, 122519464, 126667271, 147208982, 162007166, 169237545, 173392238

Offset: 1

Amiram Eldar, Oct 31 2020

			1 is a term since 1, 2 and 3 are terms of A093705.

Amiram Eldar, Table of n, a(n) for n = 1..5000

Subsequence of A338514.
Cf. A000120, A093653, A093705.
Similar sequences: A154701, A330932, A334346, A338453.

divQ[n_] := Divisible[n, DivisorSum[n, DigitCount[#, 2, 1] &]]; div = divQ /@ Range[3]; Reap[Do[If[And @@ div, Sow[k - 3]]; div = Join[Rest[div], {divQ[k]}], {k, 4, 10^7}]][[2, 1]]

cp's OEIS Frontend

A352344 Starts of runs of 3 consecutive lazy-Pell-Niven numbers (A352342).

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A352510 Starts of runs of 3 consecutive Catalan-Niven numbers (A352508).

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A364218 Starts of runs of 3 consecutive integers that are Jacobsthal-Niven numbers (A364216).

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A364381 Starts of runs of 3 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).

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A381583 Starts of runs of 3 consecutive integers that are all terms in A381581.

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A364008 Starts of runs of 3 consecutive integers that are Wythoff-Niven numbers (A364006).

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A364125 Starts of runs of 3 consecutive integers that are Stolarsky-Niven numbers (A364123).

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A331090 Positive numbers k such that -k, -(k + 1), and -(k + 2) are 3 consecutive negative negaFibonacci-Niven numbers (A331088).

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A334371 Starts of runs of 3 consecutive Moran numbers (A001101).

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