A225901 -id:A225901 - cp's OEIS frontend

A273663 Least monotonic left inverse for A273670: a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).

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

Offset: 1

Antti Karttunen, May 30 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10080

Left inverse of A273670.
Cf. A225901, A257680.
Cf. also A273662.

from sympy import factorial as f
def a007623(n, p=2): return n if nIndranil Ghosh, Jun 24 2017

a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).
Other identities.
For all n >= 0, a(A273670(n)) = n.

A275837 Permutation of nonnegative integers: a(n) = A225901(A273667(n)).

Original entry on oeis.org

0, 1, 2, 4, 18, 5, 6, 22, 12, 3, 96, 20, 72, 17, 14, 19, 114, 13, 94, 10, 11, 23, 108, 15, 24, 79, 84, 100, 101, 21, 48, 102, 8, 9, 600, 71, 480, 49, 78, 118, 119, 16, 65, 73, 98, 99, 696, 27, 360, 594, 62, 63, 70, 112, 54, 113, 74, 7, 45, 95, 552, 116, 50, 117, 672, 603, 454, 569, 37, 40, 29, 106, 444, 41, 36, 107, 85, 97, 38, 621, 86, 82, 545, 110, 528, 59, 56, 111

Offset: 0

Antti Karttunen, Aug 13 2016

Inverse: A275838.
Cf. A225901, A273667.
Cf. A275839 (fixed points).
Cf. also A275835, A275836.

(define (A275837 n) (A225901 (A273667 n)))

a(n) = A225901(A273667(n)).
Other identities. For all n >= 0:
a(n) = A266193(a(A153880(n))). [Restriction to A153880 induces the same permutation.]
A275841(n) = A273663(a(A273670(n))). [While restriction to A273670 induces another permutation.]

A275838 Permutation of nonnegative integers: a(n) = A273668(A225901(n)).

Original entry on oeis.org

0, 1, 2, 9, 3, 5, 6, 57, 32, 33, 19, 20, 8, 17, 14, 23, 41, 13, 4, 15, 11, 29, 7, 21, 24, 133, 272, 47, 293, 70, 150, 263, 152, 357, 109, 110, 74, 68, 78, 163, 69, 73, 135, 545, 249, 58, 230, 220, 30, 37, 62, 225, 100, 161, 54, 127, 86, 285, 209, 85, 182, 172, 50, 51, 197, 42, 104, 231, 105, 431, 52, 35, 12, 43, 56, 99, 213, 95, 38, 25, 134, 153, 81, 341, 26, 76

Offset: 0

Antti Karttunen, Aug 13 2016

Inverse: A275837.
Cf. A225901, A273668, A153880, A266193, A273670, A275842.
Cf. A275839 (fixed points).
Cf. also A275835, A275836.

(define (A275838 n) (A273668 (A225901 n)))

a(n) = A273668(A225901(n)).
Other identities. For all n >= 0:
a(n) = A266193(a(A153880(n))). [Restriction to A153880 induces the same permutation.]
A275842(n) = A273663(a(A273670(n))). [While restriction to A273670 induces another permutation.]

A275835 Permutation of nonnegative integers: a(n) = A273667(A225901(n)).

Original entry on oeis.org

0, 1, 6, 3, 4, 2, 56, 20, 36, 17, 21, 9, 48, 15, 30, 13, 16, 7, 18, 8, 24, 10, 12, 5, 495, 135, 74, 31, 132, 53, 582, 401, 147, 59, 157, 158, 361, 116, 216, 173, 117, 47, 136, 155, 380, 46, 78, 82, 420, 111, 61, 25, 108, 45, 490, 347, 123, 51, 133, 134, 312, 93, 192, 149, 94, 41, 112, 131, 327, 40, 64, 68, 360, 270, 80, 38, 88, 89, 416, 303, 99, 44, 109, 110, 288, 34

Offset: 0

Antti Karttunen, Aug 13 2016

Inverse: A275836.
Cf. A225901, A255411, A257684, A273667.
Cf. also A275837, A275838.

(define (A275835 n) (A273667 (A225901 n)))

a(n) = A273667(A225901(n)).
Other identities. For all n >= 0:
a(n) = A257684(a(A255411(n))). [Restriction to A255411 induces the same permutation.]

A275836 Permutation of nonnegative integers: a(n) = A225901(A273668(n)).

Original entry on oeis.org

0, 1, 5, 3, 4, 23, 2, 17, 19, 11, 21, 99, 22, 15, 111, 13, 16, 9, 18, 95, 7, 10, 118, 119, 20, 51, 101, 98, 106, 107, 14, 27, 113, 110, 85, 89, 8, 623, 75, 91, 69, 65, 115, 707, 81, 53, 45, 41, 12, 103, 659, 57, 94, 29, 615, 611, 6, 93, 579, 33, 100, 50, 603, 695, 70, 689, 112, 97, 71, 507, 616, 719, 114, 109, 26, 711, 88, 647, 46, 641, 74, 117, 47, 441, 688

Offset: 0

Antti Karttunen, Aug 13 2016

Inverse: A275835.
Cf. A225901,  A255411, A257684, A273668.
Cf. also A275837, A275838.

(define (A275836 n) (A225901 (A273668 n)))

a(n) = A225901(A273668(n)).
Other identities. For all n >= 0:
a(n) = A257684(a(A255411(n))). [Restriction to A255411 induces the same permutation.]

A275952 a(n) = A225901(A256450(A225901(n))).

Original entry on oeis.org

1, 4, 18, 19, 5, 3, 96, 97, 98, 99, 100, 101, 17, 15, 11, 9, 7, 10, 22, 23, 13, 16, 20, 21, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 65, 63, 59, 57, 55, 58, 41, 39, 35, 33, 31, 34, 46, 47, 37, 40, 44, 45, 25, 28, 42, 43, 29, 27, 94, 95, 85, 88, 92, 93, 70, 71, 61, 64, 68, 69, 49, 52

Offset: 0

Antti Karttunen, Aug 16 2016

A225901-conjugate of A256450.

Antti Karttunen, Table of n, a(n) for n = 0..5039
Index entries for sequences related to factorial base representation

Cf. A225901, A256450.

Cf. also A275954 and permutations A276011, A276012, A275841, A275842.

(define (A275952 n) (A225901 (A256450 (A225901 n))))

a(n) = A225901(A256450(A225901(n))).

A275954 a(n) = A225901(A273670(A225901(n))).

Original entry on oeis.org

1, 5, 19, 23, 2, 3, 97, 101, 115, 119, 98, 99, 6, 7, 8, 9, 10, 11, 20, 21, 14, 15, 13, 17, 601, 605, 619, 623, 602, 603, 697, 701, 715, 719, 698, 699, 606, 607, 608, 609, 610, 611, 620, 621, 614, 615, 613, 617, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 78, 79, 80, 81, 82, 83, 54, 55, 56, 57, 58, 59, 68, 69, 62, 63, 61

Offset: 0

Antti Karttunen, Aug 16 2016

A225901-conjugate of A273670.

Antti Karttunen, Table of n, a(n) for n = 0..5039
Index entries for sequences related to factorial base representation

Cf. A225901, A273670.

Cf. also A275952 and permutations A276011, A276012, A275841, A275842.

(define (A275954 n) (A225901 (A273670 (A225901 n))))

a(n) = A225901(A273670(A225901(n))).

A275957 Permutation of nonnegative integers: a(n) = A225901(A060125(n)).

Original entry on oeis.org

0, 1, 4, 3, 2, 5, 18, 19, 16, 9, 8, 17, 12, 7, 22, 21, 14, 11, 6, 13, 10, 15, 20, 23, 96, 97, 100, 99, 98, 101, 90, 91, 64, 33, 32, 65, 60, 31, 94, 93, 62, 35, 30, 61, 34, 63, 92, 95, 72, 73, 52, 27, 26, 53, 114, 115, 112, 105, 104, 113, 84, 79, 70, 45, 38, 59, 78, 85, 58, 39, 44, 71, 48, 25, 76, 75, 50, 29, 66, 43, 88, 81, 56, 41, 108, 103, 118, 117, 110, 107, 54, 37

Offset: 0

Antti Karttunen, Aug 16 2016

Inverse: A275958.
Fixed points: A275843.
Cf. A060125, A225901.

(define (A275957 n) (A225901 (A060125 n)))

a(n) = A225901(A060125(n)).

A275958 Permutation of nonnegative integers: a(n) = A060125(A225901(n)).

Original entry on oeis.org

0, 1, 4, 3, 2, 5, 18, 13, 10, 9, 20, 17, 12, 19, 16, 21, 8, 11, 6, 7, 22, 15, 14, 23, 96, 73, 52, 51, 98, 77, 42, 37, 34, 33, 44, 41, 108, 91, 64, 69, 104, 83, 102, 79, 70, 63, 110, 95, 72, 97, 76, 99, 50, 53, 90, 109, 82, 105, 68, 65, 36, 43, 40, 45, 32, 35, 78, 103, 94, 111, 62, 71, 48, 49, 100, 75, 74, 101, 66, 61, 106, 81, 92, 113, 60, 67, 112, 93, 80, 107, 30, 31

Offset: 0

Antti Karttunen, Aug 16 2016

Inverse: A275957.
Fixed points: A275843.
Cf. A060125, A225901.

(define (A275958 n) (A060125 (A225901 n)))

a(n) = A060125(A225901(n)).

A276011 Permutation of nonnegative integers: a(n) = A273662(A225901(A273670(n))).

Original entry on oeis.org

0, 3, 1, 2, 14, 17, 15, 16, 10, 13, 11, 12, 4, 5, 8, 9, 6, 7, 78, 81, 79, 80, 92, 95, 93, 94, 88, 91, 89, 90, 82, 83, 86, 87, 84, 85, 60, 63, 61, 62, 74, 77, 75, 76, 70, 73, 71, 72, 64, 65, 68, 69, 66, 67, 42, 45, 43, 44, 56, 59, 57, 58, 52, 55, 53, 54, 46, 47, 50, 51, 48, 49, 18, 19, 22, 23, 20, 21, 36, 37, 40, 41, 38, 39, 30, 31, 34, 35, 32, 33, 24, 25, 28, 29, 26, 27

Offset: 0

Antti Karttunen, Aug 16 2016

Inverse: A276012.
Cf. A225901, A273662, A273670.
Cf. also A275952 & A275954 and permutations A275841 & A275842.

(define (A276011 n) (A273662 (A225901 (A273670 n))))

a(n) = A273662(A225901(A273670(n))).

cp's OEIS Frontend

A273663 Least monotonic left inverse for A273670: a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).

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A275837 Permutation of nonnegative integers: a(n) = A225901(A273667(n)).

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A275838 Permutation of nonnegative integers: a(n) = A273668(A225901(n)).

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A275835 Permutation of nonnegative integers: a(n) = A273667(A225901(n)).

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A275836 Permutation of nonnegative integers: a(n) = A225901(A273668(n)).

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A275952 a(n) = A225901(A256450(A225901(n))).

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A275954 a(n) = A225901(A273670(A225901(n))).

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Formula

A275957 Permutation of nonnegative integers: a(n) = A225901(A060125(n)).

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Formula

A275958 Permutation of nonnegative integers: a(n) = A060125(A225901(n)).

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