A265912 Smallest m such that A014631(n) occurs in row m of Pascal's triangle.

0, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17

Offset

1,2

Comments

Each n occurs A126257(n) times consecutively.

Links

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

Example

First occurrences of z(n)=A014631(n) in the left part of Pascal's triangle, repetitions marked:
.   0: z(1)                                       [1]
.   1: *z(1)                                      [1]
.   2: *z(1)  z(2)                                [1,2]
.   3: *z(1)  z(3)                                [1,3]
.   4: *z(1)  z(4)  z(5)                          [1,4,6]
.   5: *z(1)  z(6)  z(7)                          [1,5,10]
.   6: *z(1) *z(5)  z(8)  z(9)                    [1,6,15,20]
.   7: *z(1)  z(10) z(11) z(12)                   [1,7,21,35]
.   8: *z(1)  z(13) z(14) z(15) z(16)             [1,8,28,56,70]
.   9: *z(1)  z(17) z(18) z(19) z(20)             [1,9,36,84,126]
.  10: *z(1) *z(7)  z(21) z(22) z(23) z(24)       [1,10,45,120,210,252]
.  11: *z(1)  z(25) z(26) z(27) z(28) z(29)       [1,11,55,165,330,462]
.  12: *z(1)  z(30) z(31) z(32) z(33) z(34) z(35) [1,12,66,220,495,792,924]
---------------------------------------------------------------------------
.    n: 1  2  3  4  5  6   7   8   9  10  11  12  13  14  15  16  17  18
. z(n): 1  2  3  4  6  5  10  15  20   7  21  35   8  28  56  70   9  36

Prog

(Haskell)
import Data.List (findIndex); import Data.Maybe (fromJust)
a265912 = fromJust . (flip findIndex a007318_tabl) . elem . a014631
(Python)
from itertools import count, islice
def A265912_gen(): # generator of terms
    s, c =(1, ), set()
    for i in count(0):
        for d in s:
            if d not in c:
                yield i
                c.add(d)
        s=(1, )+tuple(s[j]+s[j+1] for j in range(len(s)-1)) + ((s[-1]<<1, ) if i&1 else ())
A265912_list = list(islice(A265912_gen(), 30)) # Chai Wah Wu, Oct 17 2023

Crossrefs

Cf. A007318, A014631, A119629.

Sequence in context: A071940 A085883 A356770 * A094192 A093874 A047741

Adjacent sequences: A265909 A265910 A265911 * A265913 A265914 A265915

Keyword

nonn

Author

Reinhard Zumkeller, Dec 18 2015

Status

approved