A263273 -id:A263273 - cp's OEIS frontend

A265330 Zero-based row index to A265345; 2-adic valuation of bijective base-3 reversal of n: a(n) = A007814(A263273(n)).

0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 3

Offset: 1

Antti Karttunen, Dec 18 2015

			For n = 32, in base-3 "1012" [= A007089(32)], when we reverse it, we get "2101" [= A007089(64)], and 2-adic valuation of 64 [= "1000000" = A007088(64)] is 6, thus a(32) = 6.

Antti Karttunen, Table of n, a(n) for n = 1..6561

One less than A265331.
Cf. A007088, A007089, A263273, A265345, A265352.
Cf. A265910 (corresponding other index).
Cf. also A265336, A265337, A265340.
Differs from A007814 for the first time at n=32, where a(32) = 6, while A007814(32) = 5.

a(n) = A007814(A263273(n)).

a(2n+1) = 0, a(2n) = 1 + a(A265352(n)).

A265336 Number of nonleading 0-bits in bijective base-3 reversal of n: a(n) = A080791(A263273(n)).

Original entry on oeis.org

0, 0, 1, 0, 2, 0, 1, 1, 3, 2, 2, 2, 2, 1, 2, 2, 4, 2, 3, 1, 3, 0, 1, 1, 3, 3, 2, 1, 2, 1, 1, 3, 6, 2, 2, 4, 4, 0, 2, 2, 4, 4, 5, 3, 4, 0, 4, 1, 4, 2, 4, 3, 3, 2, 2, 1, 3, 4, 3, 5, 2, 1, 4, 2, 5, 1, 3, 3, 5, 4, 3, 3, 5, 3, 1, 2, 3, 3, 3, 2, 5, 4, 4, 4, 4, 2, 2, 4, 6, 3, 3, 2, 4, 1, 2, 3, 6, 5, 4, 3, 4, 3, 5, 0, 5, 2, 4, 2, 3, 3, 4, 2, 4, 5, 3, 4, 3, 2, 2, 2, 3, 2, 4, 4, 5, 3, 4, 2, 4

Offset: 0

Antti Karttunen, Dec 18 2015

Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A080791, A263273, A265337, A265339, A265340.

a(n) = A080791(A263273(n)).
a(0) = 0, a(2n) = 1 + a(A265339(n)), a(2n+1) = a(A265339(n)).
a(n) = A265340(n) - A265337(n).

A265337 Number of 1-bits in base-3 reversal of n: a(n) = A000120(A263273(n)).

Original entry on oeis.org

0, 1, 1, 2, 1, 3, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 1, 3, 2, 3, 2, 4, 3, 4, 2, 2, 3, 4, 3, 5, 4, 3, 1, 4, 4, 3, 2, 5, 4, 4, 2, 3, 2, 3, 3, 6, 2, 5, 2, 4, 3, 4, 3, 5, 4, 4, 3, 2, 3, 2, 4, 5, 3, 4, 1, 5, 3, 3, 2, 3, 3, 4, 2, 3, 5, 4, 3, 4, 4, 4, 2, 3, 3, 4, 3, 5, 6, 4, 2, 5, 4, 5, 4, 6, 5, 5, 2, 3, 4, 5, 3, 5, 3, 7, 3, 6, 4, 6, 4, 4, 4, 5, 3, 3, 5, 4, 5, 5, 5, 6, 4, 5, 4, 4, 3, 5, 4, 5, 4

Offset: 0

Antti Karttunen, Dec 18 2015

Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A000120, A263273, A265336, A265339, A265340.

(definec (A265337 n) (if (zero? n) 0 (+ (A265337 (A265339 n)) (if (odd? n) 1 0))))

a(n) = A000120(A263273(n)).
a(0) = 0, a(2n) = a(A265339(n)), a(2n+1) = 1 + a(A265339(n)).
a(n) = A265340(n) - A265336(n).

A265339 a(n) = A263273(A004526(A263273(n))).

Original entry on oeis.org

0, 0, 1, 1, 2, 3, 3, 2, 4, 4, 7, 9, 6, 6, 19, 10, 8, 12, 9, 7, 10, 5, 5, 19, 12, 8, 13, 13, 22, 27, 21, 18, 64, 28, 23, 36, 18, 21, 55, 11, 20, 57, 57, 24, 58, 37, 25, 30, 24, 15, 73, 31, 26, 39, 27, 22, 28, 16, 11, 64, 30, 23, 31, 14, 16, 55, 15, 20, 46, 46, 17, 58, 36, 25, 37, 17, 14, 73, 39, 26, 40, 40

Offset: 0

Antti Karttunen, Dec 18 2015

When permutation A263273 is viewed as a binary tree, a(n) gives the parent node of node containing n, for all n >= 1.

Each n occurs exactly twice in the sequence.

Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A004526, A263273, A265340.

(define (A265339 n) (A263273 (A004526 (A263273 n))))

a(n) = A263273(A004526(A263273(n))).

A265363 Permutation of nonnegative integers: a(n) = A264974(A263273(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 6, 5, 16, 9, 10, 11, 12, 13, 34, 21, 8, 25, 18, 19, 20, 15, 14, 43, 48, 17, 52, 27, 28, 29, 30, 31, 88, 33, 32, 97, 36, 37, 38, 39, 40, 115, 102, 35, 106, 63, 22, 61, 24, 23, 70, 75, 26, 79, 54, 55, 56, 57, 58, 169, 60, 59, 178, 45, 46, 47, 42, 41, 124, 129, 44, 133, 144, 49, 142, 51, 50, 151, 156, 53, 160, 81

Offset: 0

Antti Karttunen, Dec 07 2015

Composition of A263273 with the permutation obtained from its quadrisection.

Antti Karttunen, Table of n, a(n) for n = 0..6561
Index entries for sequences that are permutations of the natural numbers

Inverse: A265364.
Cf. A263273, A264974.
Cf. also A265343, A265365.

(define (A265363 n) (A264974 (A263273 n)))

a(n) = A264974(A263273(n)).
Other identities. For all n >= 0:
a(3*n) = 3*a(n).

A265364 Permutation of nonnegative integers: a(n) = A263273(A264974(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 6, 5, 16, 9, 10, 11, 12, 13, 22, 21, 8, 25, 18, 19, 20, 15, 46, 49, 48, 17, 52, 27, 28, 29, 30, 31, 34, 33, 14, 43, 36, 37, 38, 39, 40, 67, 66, 23, 70, 63, 64, 65, 24, 73, 76, 75, 26, 79, 54, 55, 56, 57, 58, 61, 60, 47, 142, 45, 136, 137, 138, 139, 148, 147, 50, 151, 144, 145, 146, 51, 154, 157, 156, 53, 160, 81

Offset: 0

Antti Karttunen, Dec 07 2015

Composition of A263273 with the permutation obtained from its quadrisection.

Antti Karttunen, Table of n, a(n) for n = 0..6561
Index entries for sequences that are permutations of the natural numbers

Inverse: A265363.
Cf. A263273, A264974.
Cf. also A265344, A265366.

(define (A265364 n) (A263273 (A264974 n)))

a(n) = A263273(A264974(n)).
Other identities. For all n >= 0:
a(3*n) = 3*a(n).

A266407 Permutation of natural numbers: a(n) = A064989(A263273((2*n)-1)).

Original entry on oeis.org

1, 2, 5, 3, 4, 17, 11, 10, 9, 7, 6, 19, 13, 8, 21, 31, 34, 71, 29, 22, 61, 25, 20, 59, 41, 18, 73, 23, 14, 33, 43, 12, 53, 37, 38, 35, 15, 26, 67, 47, 16, 157, 107, 42, 145, 55, 62, 197, 69, 68, 179, 113, 142, 129, 39, 58, 191, 137, 44, 45, 49, 122, 227, 101, 50, 199, 151, 40, 121, 57, 118, 211, 89, 82, 111, 149, 36, 91, 85

Offset: 1

Antti Karttunen, Jan 02 2016

Antti Karttunen, Table of n, a(n) for n = 1..9842
Index entries for sequences that are permutations of the natural numbers

Inverse: A266408.
Cf. A064989, A263273.
Cf. also A064216, A266401, A266403.

A030102(n) = { my(r=[n%3]); while(0M. F. Hasler's Nov 04 2011 code in A030102.
A263273 = n -> if(!n,n,A030102(n/(3^valuation(n,3))) * (3^valuation(n, 3))); \\ Taking of the quotient probably unnecessary.
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A266407 = n -> A064989(A263273((2*n)-1));
for(n=1, 9842, write("b266407.txt", n, " ", A266407(n)));

(define (A266407 n) (A064989 (A263273 (+ n n -1))))

a(n) = A064989(A263273((2*n)-1)).

A266408 Permutation of natural numbers: a(n) = (1/2) * (1+A263273(A003961(n))).

Original entry on oeis.org

1, 2, 4, 5, 3, 11, 10, 14, 9, 8, 7, 32, 13, 29, 37, 41, 6, 26, 12, 23, 15, 20, 28, 95, 22, 38, 115, 86, 19, 110, 16, 122, 30, 17, 36, 77, 34, 35, 55, 68, 25, 44, 31, 59, 60, 83, 40, 284, 61, 65, 100, 113, 33, 344, 46, 257, 70, 56, 24, 329, 21, 47, 289, 365, 88, 89, 39, 50, 49, 107, 18, 230, 27, 101, 244, 104, 112, 164, 82, 203, 174, 74

Offset: 1

Antti Karttunen, Jan 02 2016

Antti Karttunen, Table of n, a(n) for n = 1..8191
Index entries for sequences that are permutations of the natural numbers

Inverse: A266407.
Cf. A003961, A263273.
Cf. also A048673, A266401, A266403.

A030102(n) = { my(r=[n%3]); while(0M. F. Hasler's Nov 04 2011 code in A030102.
A263273 = n -> if(!n,n,A030102(n/(3^valuation(n,3))) * (3^valuation(n, 3))); \\ Taking of the quotient probably unnecessary.
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A266408 = n -> (1+A263273(A003961(n)))/2;
for(n=1, 8191, write("b266408.txt", n, " ", A266408(n)));

(define (A266408 n) (/ (+ 1 (A263273 (A003961 n))) 2))

a(n) = (1/2) * (1+A263273(A003961(n))).

A265365 Permutation of nonnegative integers: a(n) = A264978(A263273(n)).

Original entry on oeis.org

0, 1, 2, 3, 8, 7, 6, 5, 4, 9, 10, 29, 24, 26, 25, 21, 23, 22, 18, 17, 20, 15, 14, 16, 12, 11, 13, 27, 28, 83, 30, 89, 88, 87, 86, 85, 72, 71, 74, 78, 80, 79, 75, 77, 76, 63, 62, 61, 69, 68, 70, 66, 65, 67, 54, 19, 56, 51, 53, 52, 60, 59, 58, 45, 44, 47, 42, 41, 43, 48, 50, 49, 36, 35, 34, 33, 32, 31, 39, 38, 40, 81

Offset: 0

Antti Karttunen, Dec 07 2015

Composition of A263273 with the permutation obtained from its octisection.

Antti Karttunen, Table of n, a(n) for n = 0..6561
Index entries for sequences that are permutations of the natural numbers

Inverse: A265366.
Cf. A263273, A264978.
Cf. also A265363.

(define (A265365 n) (A264978 (A263273 n)))

a(n) = A264978(A263273(n)).
Other identities. For all n >= 0:
a(3*n) = 3*a(n).

A265366 Permutation of nonnegative integers: a(n) = A263273(A264978(n)).

Original entry on oeis.org

0, 1, 2, 3, 8, 7, 6, 5, 4, 9, 10, 25, 24, 26, 22, 21, 23, 19, 18, 55, 20, 15, 17, 16, 12, 14, 13, 27, 28, 11, 30, 77, 76, 75, 74, 73, 72, 217, 79, 78, 80, 67, 66, 68, 64, 63, 190, 65, 69, 71, 70, 57, 59, 58, 54, 163, 56, 165, 62, 61, 60, 47, 46, 45, 136, 52, 51, 53, 49, 48, 50, 37, 36, 109, 38, 42, 44, 43, 39, 41, 40, 81

Offset: 0

Antti Karttunen, Dec 07 2015

Composition of A263273 with the permutation obtained from its octisection.

Antti Karttunen, Table of n, a(n) for n = 0..6561
Index entries for sequences that are permutations of the natural numbers

Inverse: A265365.
Cf. A263273, A264978.
Cf. also A265364.

(define (A265366 n) (A263273 (A264978 n)))

a(n) = A263273(A264978(n)).
Other identities. For all n >= 0:
a(3*n) = 3*a(n).

cp's OEIS Frontend

A265330 Zero-based row index to A265345; 2-adic valuation of bijective base-3 reversal of n: a(n) = A007814(A263273(n)).

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A265336 Number of nonleading 0-bits in bijective base-3 reversal of n: a(n) = A080791(A263273(n)).

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A265337 Number of 1-bits in base-3 reversal of n: a(n) = A000120(A263273(n)).

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A265339 a(n) = A263273(A004526(A263273(n))).

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A265363 Permutation of nonnegative integers: a(n) = A264974(A263273(n)).

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A265364 Permutation of nonnegative integers: a(n) = A263273(A264974(n)).

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A266407 Permutation of natural numbers: a(n) = A064989(A263273((2*n)-1)).

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A266408 Permutation of natural numbers: a(n) = (1/2) * (1+A263273(A003961(n))).

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A265365 Permutation of nonnegative integers: a(n) = A264978(A263273(n)).

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