A191203 -id:A191203 - cp's OEIS frontend

A191323 Increasing sequence generated by these rules: a(1)=1, and if x is in a then [3x/2]+1 and 3x+1 are in a, where [ ]=floor.

1, 2, 4, 7, 11, 13, 17, 20, 22, 26, 31, 34, 40, 47, 52, 61, 67, 71, 79, 92, 94, 101, 103, 107, 119, 121, 139, 142, 152, 155, 157, 161, 179, 182, 184, 202, 209, 214, 229, 233, 236, 238, 242, 269, 274, 277, 283, 304, 310, 314, 322, 344, 350, 355, 358, 364, 404, 412, 416, 418, 425, 427, 457, 466, 472, 484, 517, 526, 533, 538, 547, 553

Offset: 1

Clark Kimberling, May 30 2011

nonn

This sequence represents a class of sequences generated by rules of the form "a(1)=1, and if x is in a then floor(hx+i) and floor(jx+k) are in a, where h and j are rational numbers and i and k are positive integers."  In the following examples, the floor function is denoted by [ ].
A191323:  [3x/2]+1, 3x+1
A191324:  [3x/2]+1, 3x+2
A191325:  [3x/2], [5x/2]
A191326:  [3x/2], [7x/2]
A191327:  [5x/2], [7x/2]
A191328:  [5x/3], [7x/3]
Other families of sequences generated by "rules" are listed at A191803, A191106, A101113 and A191203.

			1 -> 2,4 -> 6,7,13 -> 10,11,19,20,22,40 -> ...

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A190503, A191100, A191113, A191203.

h = 3; i = 1; j = 3; k = 1; f = 1; g = 12;
a=Union[Flatten[NestList[{Floor[h#/2]+i,j#+k}&,f,g]]]
(* A191323 *)

A191211 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 1+2x and 1+x^2 are in a.

Original entry on oeis.org

1, 2, 3, 5, 7, 10, 11, 15, 21, 23, 26, 31, 43, 47, 50, 53, 63, 87, 95, 101, 107, 122, 127, 175, 191, 203, 215, 226, 245, 255, 351, 383, 407, 431, 442, 453, 491, 511, 530, 677, 703, 767, 815, 863, 885, 907, 962, 983, 1023, 1061, 1355, 1407, 1535, 1631, 1727, 1771, 1815, 1850, 1925, 1967, 2047, 2123, 2210, 2501

Offset: 1

Clark Kimberling, May 29 2011

nonn

See A191203.

			1 -> 2,3 -> 5,7,10 ->

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A191203.

import Data.Set (singleton, deleteFindMin, insert)
a191211 n = a191211_list !! (n-1)
a191211_list = f $ singleton 1 where
   f s = m : f (insert (2 * m + 1) $ insert (m ^ 2 + 1) s')
         where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Apr 18 2014

g = 11; Union[Flatten[NestList[{1 + 2 #, 1 + #^2} &, 1, g]]]
(* A191211; use g>10 to get all of first 60 terms *)

A191281 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x and x^2-x+1 are in a.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 24, 26, 28, 31, 32, 43, 48, 52, 56, 57, 62, 64, 86, 96, 104, 112, 114, 124, 128, 133, 157, 172, 183, 192, 208, 224, 228, 241, 248, 256, 266, 314, 344, 366, 384, 416, 448, 456, 482, 496, 512, 532, 553, 628, 651, 688, 732, 757, 768, 832, 896, 912, 931, 964, 992, 993, 1024, 1064, 1106, 1256, 1302

Offset: 1

Clark Kimberling, May 29 2011

nonn

See A191203.

			1 -> 2 -> 3,4 -> 6,7,8,13 ->

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191203.

g = 12; Union[Flatten[NestList[{2 #, #^2 - # + 1} &, 1, g]]]
(* A191281; use g>11 to get all of first 60 terms *)

A191282 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x and x^2+x+1 are in a.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 32, 42, 43, 48, 52, 56, 57, 64, 73, 84, 86, 96, 104, 112, 114, 128, 146, 157, 168, 172, 183, 192, 208, 211, 224, 228, 256, 273, 292, 314, 336, 344, 366, 384, 416, 422, 448, 456, 463, 512, 546, 584, 601, 628, 672, 688, 703, 732, 768, 813, 832, 844, 896, 912, 926, 1024, 1057, 1092

Offset: 1

Clark Kimberling, May 29 2011

nonn

See A191203.

			1 -> 2,3 -> 4,6,7,13 ->

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191203.

g = 11; Union[Flatten[NestList[{2 #, #^2 + # + 1} &, 1, g]]]
(* A191282; use g>10 to get all of first 60 terms *)

A191283 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x and x(x+1)/2 are in a.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 10, 12, 16, 20, 21, 24, 32, 36, 40, 42, 48, 55, 64, 72, 78, 80, 84, 96, 110, 128, 136, 144, 156, 160, 168, 192, 210, 220, 231, 256, 272, 288, 300, 312, 320, 336, 384, 420, 440, 462, 512, 528, 544, 576, 600, 624, 640, 666, 672, 768, 820, 840, 880, 903, 924, 1024, 1056, 1088, 1152, 1176, 1200, 1248, 1280, 1332

Offset: 1

Clark Kimberling, May 29 2011

nonn

See A191203.

			1 -> 2 -> 3,4 -> 6,8,10 ->

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191203.

g = 12; Union[Flatten[NestList[{2 #, (#^2 + #)/2} &, 1, g]]]
(* A191283; use g>10 to get all of first 60 terms *)

A191284 Increasing sequence generated by these rules: a(1)=1, and if x is in a then floor(3x/2) and 2x are in a.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 19, 24, 26, 27, 28, 32, 36, 38, 39, 40, 42, 48, 52, 54, 56, 57, 58, 60, 63, 64, 72, 76, 78, 80, 81, 84, 85, 87, 90, 94, 96, 104, 108, 112, 114, 116, 117, 120, 121, 126, 127, 128, 130, 135, 141, 144, 152, 156, 160, 162, 168, 170, 171, 174, 175, 180, 181, 188, 189, 190, 192, 195, 202, 208, 211, 216

Offset: 1

Clark Kimberling, May 29 2011

nonn

See A191203.

			1 -> 2,3 -> 4,6 -> 8,9,12 ->

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191203.

g=16; Union[Flatten[NestList[{Floor[3 #/2], 2#} &, 1, g]]]
(* A191284; use g>15 to get all of first 60 terms *)

A191285 Increasing sequence S generated by these rules: 1 is in S, and if x is in S then 3x and floor((x^2)/2) are in S.

Original entry on oeis.org

0, 1, 3, 4, 8, 9, 12, 24, 27, 32, 36, 40, 72, 81, 96, 108, 120, 216, 243, 288, 324, 360, 364, 512, 648, 729, 800, 864, 972, 1080, 1092, 1536, 1944, 2187, 2400, 2592, 2916, 3240, 3276, 3280, 4608, 5832, 6561, 7200, 7776, 8748, 9720, 9828, 9840, 13824, 17496, 19683, 21600, 23328, 26244, 29160, 29484, 29520, 29524

Offset: 1

Clark Kimberling, May 29 2011

nonn

See A191203.

			1 -> 0,3 -> 4,8,9,27 ->

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191203.

g=12; Union[Flatten[NestList[{3#,Floor[(#^2)/2]}&,1,g]]]
(* A191285; use g>11 to get all of first 60 terms *)

A191286 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x and 1+x^2 are in a.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 10, 15, 18, 26, 27, 30, 37, 45, 54, 78, 81, 82, 90, 101, 111, 135, 162, 226, 234, 243, 246, 270, 303, 325, 333, 405, 486, 677, 678, 702, 729, 730, 738, 810, 901, 909, 975, 999, 1215, 1370, 1458, 2026, 2031, 2034, 2106, 2187, 2190, 2214, 2430, 2703, 2727, 2917, 2925, 2997, 3645, 4110, 4374

Offset: 1

Clark Kimberling, May 29 2011

nonn

See A191203.

			1 -> 2,3 -> 5,6,9,10 ->

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191203.

g = 10; Union[Flatten[NestList[{3 #, 1 + #^2} &, 1, g]]]
(* A191286; use g>9 to get all of first 60 terms *)

A191287 Increasing sequence generated by these rules: a(1)=1, and if x is in a then floor(3x/2) and 3x are in a.

Original entry on oeis.org

1, 3, 4, 6, 9, 12, 13, 18, 19, 27, 28, 36, 39, 40, 42, 54, 57, 58, 60, 63, 81, 84, 85, 87, 90, 94, 108, 117, 120, 121, 126, 127, 130, 135, 141, 162, 171, 174, 175, 180, 181, 189, 190, 195, 202, 211, 243, 252, 255, 256, 261, 262, 270, 271, 282, 283, 285, 292, 303, 316, 324, 351, 360, 363, 364, 378, 381, 382, 384, 390, 391, 393, 405

Offset: 1

Clark Kimberling, May 29 2011

nonn

See A191203.

			1 -> 3 -> 4,9 -> 6,12,13,27 ->

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191203.

g=15; Union[Flatten[NestList[{Floor[3#/2],3#} &, 1, g]]]
(* A191287; use g>14 to get all of first 60 terms *)

A191288 Increasing sequence generated by these rules: 1 is in a, and if x is in a then 2x and floor((x^2)/3) are in a.

Original entry on oeis.org

0, 1, 2, 4, 5, 8, 10, 16, 20, 21, 32, 33, 40, 42, 64, 66, 80, 84, 85, 128, 132, 133, 147, 160, 168, 170, 256, 264, 266, 294, 320, 336, 340, 341, 363, 512, 528, 532, 533, 588, 640, 672, 680, 682, 726, 1024, 1056, 1064, 1066, 1176, 1280, 1344, 1360, 1364, 1365, 1452, 2048, 2112, 2128, 2132, 2133, 2352, 2408, 2560, 2688, 2720

Offset: 1

Clark Kimberling, May 29 2011

nonn

See A191203.

			1 -> {0,2} -> 4 -> {5,8} -> {10,16,21} -> ...

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A191203.

g=13; Union[Flatten[NestList[{2#, Floor[(#^2)/3]}&,1,g]]]
(* A191288; use g>12 to get all of first 60 terms *)

Definition corrected by Han Guoniu, Oct 11 2012

cp's OEIS Frontend

A191323 Increasing sequence generated by these rules: a(1)=1, and if x is in a then [3x/2]+1 and 3x+1 are in a, where [ ]=floor.

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A191211 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 1+2x and 1+x^2 are in a.

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A191281 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x and x^2-x+1 are in a.

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A191282 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x and x^2+x+1 are in a.

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A191283 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x and x(x+1)/2 are in a.

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A191284 Increasing sequence generated by these rules: a(1)=1, and if x is in a then floor(3x/2) and 2x are in a.

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A191285 Increasing sequence S generated by these rules: 1 is in S, and if x is in S then 3x and floor((x^2)/2) are in S.

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A191286 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x and 1+x^2 are in a.

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