A084107 -id:A084107 - cp's OEIS frontend

A083942 Positions of breadth-first-wise encodings (A002542) of the complete binary trees (A084107) in A014486.

0, 1, 8, 625, 13402696, 19720133460129649, 126747521841153485025455279433135688, 15141471069096667541622192498608408980462133134430650704600552060872705905

Offset: 0

Antti Karttunen, May 13 2003

nonn

Alexander Adamchuk, Nov 10 2007, Table of n, a(n) for n = 0..11
Eric Weisstein's World of Mathematics, Catalan Number.

Cf. A014138 (partial sums of Catalan numbers), A000108 (Catalan Numbers).

a(n) = A057118(A084108(n)).
a(n) = A080300(A002542(n)) [provided that 2^((2^n)-1)*((2^((2^n)-1))-1) is indeed the formula for A002542].
Conjecture: a(n) = A014138(2^n-2) for n>0. - Alexander Adamchuk, Nov 10 2007
Conjecture: a(n) = Sum_{k=1..2^n-1} A000108(k). - Alexander Adamchuk, Nov 10 2007
Let h(n) = -((C(2*n,n)*hypergeom([1,1/2+n],[2+n],4))/(1+n)+I*sqrt(3)/2+1/2). Assuming Adamchuk's conjecture a(n) = h(2^n) and A014138(n) = h(n+1). - Peter Luschny, Mar 09 2015

A084108 A014486-indices of "Complete Binary Trees".

Original entry on oeis.org

0, 1, 6, 477, 11231586, 17656351387745509, 118547604486270210927391203275078974, 14557702344245589436016960628730576845591277100880695377777962217288601549

Offset: 0

Antti Karttunen, May 13 2003

nonn

Fixed points of permutations A069767 and A069768.

a(n) = A057117(A083942(n)). Also iterates of A080298, i.e., a(1)=A080298(0), a(2)=A080298(A080298(0)), a(3)=A080298(A080298(A080298(0))), etc. Cf. also A083940, A080274.

a(n) = A080300(A084107(n)).

A356082 Matula-Goebel number of the complete binary tree of n levels.

Original entry on oeis.org

1, 4, 49, 51529, 400034745289, 135016053798647886015597889

Offset: 1

Kevin Ryde, Jul 26 2022

An estimate for a(7) is 7.304058*10^55. - Hugo Pfoertner, Jul 26 2022

			For n=3, the complete binary tree of 3 levels is
        49
      /    \     a(3) = prime(4)^2
    4       4         = 49
   / \     / \
  1   1   1   1

Cf. A006894 (Colijn-Plazzotta), A084107 (balanced binary).

Cf. A356083 (ternary), A356084 (quaternary).

a(n) = my(ret=1); for(i=2,n, ret=prime(ret)^2); ret;

a(n) = prime(a(n-1))^2, for n>=2.

a(6) from Rémy Sigrist, Jul 26 2022

A083941 A014486-encoding of symmetric binary trees.

Original entry on oeis.org

0, 2, 50, 844, 906, 13624, 13876, 14642, 14892, 15402, 218352, 219368, 222436, 223448, 225492, 234722, 235730, 238796, 239800, 241844, 246986, 247986, 250028, 254122, 3494880, 3498960, 3511240, 3515312, 3523496, 3560388, 3564452, 3576728

Offset: 0

Antti Karttunen, May 13 2003

nonn

Subsets: A084107, A080263, A080293.

a(n) = A014486(A083940(n)).

cp's OEIS Frontend

A083942 Positions of breadth-first-wise encodings (A002542) of the complete binary trees (A084107) in A014486.

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A084108 A014486-indices of "Complete Binary Trees".

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A356082 Matula-Goebel number of the complete binary tree of n levels.

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A083941 A014486-encoding of symmetric binary trees.

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