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

%I A265912 #8 Oct 17 2023 19:18:27
%S A265912 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,
%T A265912 12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,14,15,15,15,15,
%U A265912 15,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17
%N A265912 Smallest m such that A014631(n) occurs in row m of Pascal's triangle.
%C A265912 Each n occurs A126257(n) times consecutively.
%H A265912 Reinhard Zumkeller, <a href="/A265912/b265912.txt">Table of n, a(n) for n = 1..10000</a>
%e A265912 First occurrences of z(n)=A014631(n) in the left part of Pascal's triangle, repetitions marked:
%e A265912 .   0: z(1)                                       [1]
%e A265912 .   1: *z(1)                                      [1]
%e A265912 .   2: *z(1)  z(2)                                [1,2]
%e A265912 .   3: *z(1)  z(3)                                [1,3]
%e A265912 .   4: *z(1)  z(4)  z(5)                          [1,4,6]
%e A265912 .   5: *z(1)  z(6)  z(7)                          [1,5,10]
%e A265912 .   6: *z(1) *z(5)  z(8)  z(9)                    [1,6,15,20]
%e A265912 .   7: *z(1)  z(10) z(11) z(12)                   [1,7,21,35]
%e A265912 .   8: *z(1)  z(13) z(14) z(15) z(16)             [1,8,28,56,70]
%e A265912 .   9: *z(1)  z(17) z(18) z(19) z(20)             [1,9,36,84,126]
%e A265912 .  10: *z(1) *z(7)  z(21) z(22) z(23) z(24)       [1,10,45,120,210,252]
%e A265912 .  11: *z(1)  z(25) z(26) z(27) z(28) z(29)       [1,11,55,165,330,462]
%e A265912 .  12: *z(1)  z(30) z(31) z(32) z(33) z(34) z(35) [1,12,66,220,495,792,924]
%e A265912 ---------------------------------------------------------------------------
%e A265912 .    n: 1  2  3  4  5  6   7   8   9  10  11  12  13  14  15  16  17  18
%e A265912 . z(n): 1  2  3  4  6  5  10  15  20   7  21  35   8  28  56  70   9  36
%o A265912 (Haskell)
%o A265912 import Data.List (findIndex); import Data.Maybe (fromJust)
%o A265912 a265912 = fromJust . (flip findIndex a007318_tabl) . elem . a014631
%o A265912 (Python)
%o A265912 from itertools import count, islice
%o A265912 def A265912_gen(): # generator of terms
%o A265912     s, c =(1,), set()
%o A265912     for i in count(0):
%o A265912         for d in s:
%o A265912             if d not in c:
%o A265912                 yield i
%o A265912                 c.add(d)
%o A265912         s=(1,)+tuple(s[j]+s[j+1] for j in range(len(s)-1)) + ((s[-1]<<1,) if i&1 else ())
%o A265912 A265912_list = list(islice(A265912_gen(),30)) # _Chai Wah Wu_, Oct 17 2023
%Y A265912 Cf. A007318, A014631, A119629.
%K A265912 nonn
%O A265912 1,2
%A A265912 _Reinhard Zumkeller_, Dec 18 2015