A344344 -id:A344344 - cp's OEIS frontend

A344341 Gray-code Niven numbers: numbers divisible by the number of 1's in their binary reflected Gray code (A005811).

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 15, 16, 20, 24, 27, 28, 30, 31, 32, 33, 36, 39, 40, 42, 44, 45, 48, 51, 52, 56, 57, 60, 62, 63, 64, 68, 72, 75, 76, 80, 84, 88, 90, 92, 96, 99, 100, 104, 105, 108, 111, 112, 116, 120, 123, 124, 126, 127, 128, 129, 132, 135, 136

Offset: 1

Amiram Eldar, May 15 2021

			2 is a term since its Gray code is 11 and 1+1 = 2 is a divisor of 2.
6 is a term since its Gray code is 101 and 1+0+1 = 2 is a divisor of 6.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Gray Code.
Wikipedia, Gray code.

Cf. A005811, A014550.
Subsequences: A344342, A344343, A344344.
Similar sequences: A005349 (decimal), A049445 (binary), A064150 (ternary), A064438 (quaternary), A064481 (base 5), A118363 (factorial), A328208 (Zeckendorf), A328212 (lazy Fibonacci), A331085 (negaFibonacci), A333426 (primorial), A334308 (base phi), A331728 (negabinary), A342426 (base 3/2), A342726 (base i-1).

gcNivenQ[n_] := Divisible[n, DigitCount[BitXor[n, Floor[n/2]], 2, 1]]; Select[Range[150], gcNivenQ]

A344342 Numbers k such that k and k + 1 are both Gray-code Niven numbers (A344341).

Original entry on oeis.org

1, 2, 3, 6, 7, 8, 14, 15, 27, 30, 31, 32, 39, 44, 51, 56, 62, 63, 75, 99, 104, 111, 123, 126, 127, 128, 135, 144, 155, 159, 174, 175, 184, 185, 195, 204, 207, 215, 224, 231, 234, 235, 243, 244, 248, 254, 255, 264, 275, 284, 294, 300, 304, 305, 315, 335, 354, 375

Offset: 1

Amiram Eldar, May 15 2021

			1 is a term since 1 and 2 are both Gray-code Niven numbers.

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

Cf. A005811, A014550.
Subsequence of: A344341.
Subsequences: A344343 and A344344.
Similar sequences: A330927 (decimal), A328205 (factorial), A328209 (Zeckendorf), A328213 (lazy Fibonacci), A330931 (binary), A331086 (negaFibonacci), A333427 (primorial), A334309 (base phi), A331820 (negabinary), A342427 (base 3/2).

gcNivenQ[n_] := Divisible[n, DigitCount[BitXor[n, Floor[n/2]], 2, 1]]; Select[Range[400], And @@ gcNivenQ[# + {0, 1}] &]

A344343 Starts of runs of 3 consecutive Gray-code Niven numbers (A344341).

Original entry on oeis.org

1, 2, 6, 7, 14, 30, 31, 62, 126, 127, 174, 184, 234, 243, 254, 304, 474, 483, 510, 511, 534, 543, 544, 783, 784, 903, 904, 954, 963, 1022, 1134, 1144, 1253, 1264, 1448, 1475, 1504, 1895, 1914, 1923, 1974, 2046, 2047, 2093, 2094, 2104, 2814, 2888, 2944, 3054, 3064

Offset: 1

Amiram Eldar, May 15 2021

			1 is a term since 1, 2 and 3 are all Gray-code Niven numbers.

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

Cf. A005811, A014550.
Subsequence of A344341 and A344342.
Subsequences: A344344.
Similar sequences: A154701 (decimal), A328206 (factorial), A328210 (Zeckendorf), A328214 (lazy Fibonacci), A330932 (binary), A331087 (negaFibonacci), A333428 (primorial), A334310 (base phi), A331822 (negabinary), A342428 (base 3/2).

gcNivenQ[n_] := Divisible[n, DigitCount[BitXor[n, Floor[n/2]], 2, 1]]; Select[Range[3000], AllTrue[# + {0, 1, 2}, gcNivenQ] &]

A352092 Starts of runs of 4 consecutive tribonacci-Niven numbers (A352089).

Original entry on oeis.org

1602, 218349, 296469, 1213749, 1291869, 1896630, 1952070, 2153709, 2399550, 3149109, 3753870, 3809310, 3983229, 4226208, 4256790, 4449288, 4711482, 5707897, 5727708, 6141750, 6589230, 6969429, 7205757, 7229208, 7276143, 7292943, 7454710, 7752588, 7937109, 8877069

Offset: 1

Amiram Eldar, Mar 04 2022

Conjecture: There are no runs of 5 consecutive tribonacci-Niven numbers (checked up to 10^10).

			1602 is a term since 1602, 1603, 1604 and 1605 are all divisible by the number of terms in their minimal tribonacci representation:
     k    A278038(k)  A278043(k)  k/A278043(k)
  --------------------------------------------
  1602  110100011010           6           267
  1603  110100011011           7           229
  1604  110100100000           4           401
  1605  110100100001           5           321

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

Cf. A278038, A278043.
Subsequence of A352089, A352090 and A352091.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344.

t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; triboNivenQ[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; Divisible[n, DigitCount[Total[2^(s - 1)], 2, 1]]]; seq[count_, nConsec_] := Module[{tri = triboNivenQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ tri, c++; AppendTo[s, k - nConsec]]; tri = Join[Rest[tri], {triboNivenQ[k]}]; k++]; s]; seq[6, 4]

A352110 Starts of runs of 4 consecutive lazy-tribonacci-Niven numbers (A352107).

Original entry on oeis.org

1081455, 1976895, 2894175, 5886255, 6906912, 15604110, 16588752, 19291479, 20387232, 25919439, 32394942, 34801557, 35654175, 36813582, 36907899, 39117219, 41407392, 43520832, 46181055, 47954499, 52145952, 54524319, 54815397, 56733639, 57775102, 58942959, 59292177

Offset: 1

Amiram Eldar, Mar 05 2022

Conjecture: There are no runs of 5 consecutive lazy-tribonacci-Niven numbers (checked up to 6*10^9).

			1081455 is a term since 1081455, 1081456, 1081457 and 1081458 are all divisible by the number of terms in their maximal tribonacci representation:
        k               A352103(k)   A352104(k)    k/A352104(k)
  -------  -----------------------   ----------    ------------
  1081455  10101011011110110011110           15           72097
  1081456  10101011011110110011111           16           67591
  1081457  10101011011110110100100           13           83189
  1081458  10101011011110110100101           14           77247

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

Cf. A352103, A352104.
Subsequence of A352107, A352108 and A352109.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092.

A352345 Starts of runs of 4 consecutive lazy-Pell-Niven numbers (A352342).

Original entry on oeis.org

750139, 41765247, 54831951, 56423275, 136038447, 151175724, 223956843, 227483124, 293913170, 362557214, 382572475, 457616575, 502106253, 562407324, 586380624, 637133390, 724382239, 771849439, 774421478, 859463253, 926398647, 953750523, 1043787390, 1193063550

Offset: 1

Amiram Eldar, Mar 12 2022

Conjecture: There are no runs of 5 consecutive lazy-Pell-Niven numbers (checked up to 10^9).

			750139 is a term since 750139, 750140, 750141 and 750142 are all divisible by the sum of the digits in their maximal Pell representation:
       k        A352339(k)  A352340(k)  k/A352340(k)
  ------  ----------------  ---------   -----------
  750139  1102022021112220         19         39481
  750140  1102022021112221         20         37507
  750141  1102022021112222         21         35721
  750142  1102022021120210         17         44126

Cf. A352339, A352340.
Subsequence of A352342, A352343 and A352344.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110.

A352511 Starts of runs of 4 consecutive Catalan-Niven numbers (A352508).

Original entry on oeis.org

144, 15630, 164862, 202761, 373788, 450189, 753183, 1403961, 1779105, 2588415, 2673774, 2814229, 2850880, 3009174, 3013722, 3045870, 3091023, 3702390, 3942519, 4042950, 4432128, 4725432, 4938348, 5718942, 5907312, 6268248, 6519615, 6592752, 6791379, 7095492, 8567802

Offset: 1

Amiram Eldar, Mar 19 2022

Conjecture: There are no runs of 5 consecutive Catalan-Niven numbers (checked up to 10^9).

			144 is a term since 144, 145, 146 and 147 are all divisible by the sum of the digits in their Catalan representation:
    k  A014418(k)  A014420(k)  k/A014420(k)
  ---  ----------  ----------  ------------
  144      100210           4            36
  145      100211           5            29
  146      101000           2            73
  147      101001           3            49

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

Cf. A000108, A014418, A014420.
Subsequence of A352508, A352509 and A352510.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345.

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[5, 4]

A364219 Starts of runs of 4 consecutive integers that are Jacobsthal-Niven numbers (A364216).

Original entry on oeis.org

1, 42, 43, 2731, 11605, 13024, 14229, 25983, 39390, 45727, 46624, 47529, 60073, 96039, 111390, 131103, 132010, 133984, 134430, 140767, 148180, 148181, 148509, 174762, 174763, 187744, 197790, 237609, 247114, 266453, 275229, 287988, 312190, 330847, 354429, 370269

Offset: 1

Amiram Eldar, Jul 14 2023

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

Subsequence of A364216, A364217 and A364218.
Subsequences: A364220, A364221.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345, A352511.

consecJacobsthalNiven[4*10^5, 4] (* using the function from A364217 *)

lista(4*10^5, 4) \\ using the function from A364217

A364382 Starts of runs of 4 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).

Original entry on oeis.org

1, 2, 3, 8, 9, 42, 43, 84, 85, 2730, 2731, 5460, 5461, 21864, 21865, 59477, 60073, 66303, 75048, 112509, 156607, 174762, 174763, 283327, 312190, 320768, 349524, 349525, 351570, 354429, 374589, 384039, 479037, 504510, 527103, 624040, 625470, 656829, 688830, 711423

Offset: 1

Amiram Eldar, Jul 21 2023

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

Cf. A265745, A265747.
Subsequence of A364379, A364380 and A364381.
A364383 is a subsequence.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345, A352511, A364219.

consecGreedyJN[72000, 4] (* using the function consecGreedyJN from A364380 *)

lista(10^5, 4) \\ using the function lista from A364380

A364126 Starts of runs of 4 consecutive integers that are Stolarsky-Niven numbers (A364123).

Original entry on oeis.org

125340, 945591, 14998632, 16160505, 19304934, 42053801, 42064137, 46049955, 57180537, 103562368, 108489885, 122495982, 135562299, 139343337, 147991452, 164002374, 271566942, 296019657, 301748706, 310980030, 314537247, 316725570, 333478935, 336959907, 349815255

Offset: 1

Amiram Eldar, Jul 07 2023

Are there runs of 5 or more consecutive integers that are Stolarsky-Niven numbers?

Amiram Eldar, Table of n, a(n) for n = 1..207

Subsequence of A364123, A364124 and A364125.

Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345, A352511.

seq[2, 4] (* generates the first 2 terms, using the function seq[count, nConsec] from A364124 *)

lista(2, 4) \\ generates the first 2 terms, using the function lista(count, nConsec) from A364124

cp's OEIS Frontend

A344341 Gray-code Niven numbers: numbers divisible by the number of 1's in their binary reflected Gray code (A005811).

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A344342 Numbers k such that k and k + 1 are both Gray-code Niven numbers (A344341).

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A344343 Starts of runs of 3 consecutive Gray-code Niven numbers (A344341).

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A352092 Starts of runs of 4 consecutive tribonacci-Niven numbers (A352089).

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A352110 Starts of runs of 4 consecutive lazy-tribonacci-Niven numbers (A352107).

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A352345 Starts of runs of 4 consecutive lazy-Pell-Niven numbers (A352342).

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A352511 Starts of runs of 4 consecutive Catalan-Niven numbers (A352508).

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A364219 Starts of runs of 4 consecutive integers that are Jacobsthal-Niven numbers (A364216).

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A364382 Starts of runs of 4 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).

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