A273663 -id:A273663 - cp's OEIS frontend

A276951 Index of column where n is located in array A276953 (equally: row in A276955).

0, 1, 1, 2, 3, 4, 1, 5, 2, 6, 7, 8, 3, 9, 4, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 19, 5, 20, 21, 22, 2, 23, 6, 24, 25, 26, 7, 27, 8, 28, 29, 30, 31, 32, 33, 34, 35, 36, 3, 37, 9, 38, 39, 40, 4, 41, 10, 42, 43, 44, 11, 45, 12, 46, 47, 48, 49, 50, 51, 52, 53, 54, 13, 55, 14, 56, 57, 58, 15, 59, 16, 60, 61, 62, 17, 63, 18, 64

Offset: 0

Antti Karttunen, Sep 22 2016

a(0) = 0 by convention, because 0 is not present in arrays A276953 and A276955.

Antti Karttunen, Table of n, a(n) for n = 0..5040
Index entries for sequences related to factorial base representation

Cf. A260736, A266193, A273670, A276950, A276952, A273663.
Cf. arrays A276953 & A276955. A276949 gives their other index.
Cf. also A257681, A275847.

(definec (A276951 n) (cond ((zero? n) n) ((not (zero? (A276950 n))) (A276952 n)) (else (A276951 (A266193 n)))))

a(0) = 0; for n >= 1, if A260736(n) > 0 [when A276950(n) is not zero, when n is in A273670], then a(n) = A276952(n) = 1 + A273663(n), otherwise a(n) = a(A266193(n)).
Other identities. For all n >= 0:
a(n) = A257681(A275847(n)).

A275845 Permutation of natural numbers: a(0) = 0, a(A153880(n)) = A255411(n), a(A273670(n)) = A256450(a(n)).

Original entry on oeis.org

0, 1, 4, 2, 6, 3, 12, 8, 16, 5, 15, 10, 18, 21, 22, 7, 20, 13, 24, 27, 28, 9, 26, 17, 48, 30, 52, 33, 34, 11, 60, 32, 64, 23, 56, 36, 66, 61, 70, 39, 40, 14, 73, 38, 78, 29, 67, 42, 72, 80, 76, 74, 85, 45, 84, 46, 88, 19, 89, 44, 90, 97, 94, 35, 81, 49, 87, 99, 93, 91, 105, 53, 96, 104, 100, 54, 109, 25, 108, 110, 112, 51, 111, 121, 114, 117, 118, 41

Offset: 0

Antti Karttunen, Aug 13 2016

Inverse: A275846.
Cf. A000142, A052849, A153880, A225901, A255411, A256450, A257680, A266193, A273663, A273670.
Similar permutations: A273667 (a more recursed variant), A275847, A275848.

a(0) = 0; for n >= 1: if A257680(A225901(n)) = 0 [when n is one of the terms of A153880] then a(n) = A255411(A266193(n)), otherwise [when n is one of the terms of A273670], a(n) = A256450(a(A273663(n))).
Other identities:
a(A000142(n)) = A052849(n) for all n >= 2.

A273665 a(0) = 0; for n >= 1: if n = A153880(k) for some k, then a(n) = 2a(k), otherwise, n = A273670(h) for some h, and a(n) = 1 + 2a(h).

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 4, 11, 6, 15, 9, 23, 10, 13, 14, 31, 19, 47, 21, 27, 29, 63, 39, 95, 8, 43, 22, 55, 59, 127, 12, 79, 30, 191, 17, 87, 18, 45, 46, 111, 119, 255, 25, 159, 61, 383, 35, 175, 20, 37, 26, 91, 93, 223, 28, 239, 62, 511, 51, 319, 38, 123, 94, 767, 71, 351, 41, 75, 53, 183, 187, 447, 42, 57, 54, 479, 125, 1023, 58

Offset: 0

Antti Karttunen, May 30 2016

Inverse: A273666.
Cf. A153880, A225901, A257680, A266193, A273663, A273670.
Related or similar permutations: A255565, A273667.

a(0) = 0; for n >= 1: if A257680(A225901(n)) = 0 [i.e., n is one of the terms of A153880], then a(n) = 2*a(A266193(n)), otherwise [when n is one of the terms of A273670], a(n) = 1 + 2*a(A273663(n)).

A276952 Partial sums of A276950.

Original entry on oeis.org

0, 1, 1, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 18, 19, 19, 20, 21, 22, 22, 23, 23, 24, 25, 26, 26, 27, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 37, 37, 38, 39, 40, 40, 41, 41, 42, 43, 44, 44, 45, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 54, 55, 55, 56, 57, 58, 58, 59, 59, 60, 61

Offset: 0

Antti Karttunen, Sep 22 2016

Each n occurs A276948(n) times.

Antti Karttunen, Table of n, a(n) for n = 0..5040
Index entries for sequences related to factorial base representation

One more than A273663.

Cf. also A276948, A276951, A257682.

(define (A276952 n) (+ 1 (A273663 n)))
(definec (A276952 n) (if (zero? n) n (+ (A276950 n) (A276952 (- n 1)))))

a(0) = 0; for n >= 1, a(n) = A276950(n) + a(n-1).
Other identities. For all n >= 1:
a(n) = 1 + A273663(n).

A276957 Permutation of natural numbers: a(A153880(n)) = A255411(n), a(A273670(n)) = A256450(n).

Original entry on oeis.org

1, 4, 2, 3, 5, 12, 6, 16, 7, 8, 9, 18, 10, 22, 11, 13, 14, 15, 17, 19, 20, 21, 23, 48, 24, 52, 25, 26, 27, 60, 28, 64, 29, 30, 31, 66, 32, 70, 33, 34, 35, 36, 37, 38, 39, 40, 41, 72, 42, 76, 43, 44, 45, 84, 46, 88, 47, 49, 50, 90, 51, 94, 53, 54, 55, 56, 57, 58, 59, 61, 62, 96, 63, 100, 65, 67, 68, 108, 69, 112, 71, 73

Offset: 1

Antti Karttunen, Sep 22 2016

Inverse: A276958.
Cf. A276950, A255411, A256450, A266193, A273663.
For more recursed variants see: A275845, A275847 & A273667.

(define (A276957 n) (cond ((zero? n) n) ((zero? (A276950 n)) (A255411 (A266193 n))) (else (A256450 (A273663 n)))))

If A276950(n) = 0, then a(n) = A255411(A266193(n)), otherwise a(n) = A256450(A273663(n)).

cp's OEIS Frontend

A276951 Index of column where n is located in array A276953 (equally: row in A276955).

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Formula

A275845 Permutation of natural numbers: a(0) = 0, a(A153880(n)) = A255411(n), a(A273670(n)) = A256450(a(n)).

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Formula

A273665 a(0) = 0; for n >= 1: if n = A153880(k) for some k, then a(n) = 2*a(k), otherwise, n = A273670(h) for some h, and a(n) = 1 + 2*a(h).

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Formula

A276952 Partial sums of A276950.

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Author

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Programs

Scheme

Formula

A276957 Permutation of natural numbers: a(A153880(n)) = A255411(n), a(A273670(n)) = A256450(n).

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Author

Keywords

Links

Crossrefs

Programs

Scheme

Formula

A273665 a(0) = 0; for n >= 1: if n = A153880(k) for some k, then a(n) = 2a(k), otherwise, n = A273670(h) for some h, and a(n) = 1 + 2a(h).