cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A276949 Index of row where n is located in array A276953 (equally: column in A276955).

Original entry on oeis.org

0, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5
Offset: 0

Views

Author

Antti Karttunen, Sep 22 2016

Keywords

Comments

This is the smallest difference that occurs between any nonzero digit's radix (which is one more than its one-based position from the right) and that digit's value in the factorial base representation of n. See A225901 and the example.
a(0) = 0 by convention, as there are no nonzero digits present, and neither does 0 occur in arrays A276953 & A276955.

Examples

			For n=8, its factorial base representation (A007623) is "110", where the radix for each digit position 1, 2, 3 (from the right) is 2, 3, 4 (one larger than the position). For the 1 in the middle position the difference is 3-1 = 2, while for the 1 at the left we obtain 4-1 = 3. Of these two differences 2 is smaller, thus a(8)=2.

Links

Crossrefs

Cf. A007623, A257679, A266193, A276950.
Cf. A276951 (for the other index).
Cf. arrays A276953 & A276955.
Cf. also A225901, A273667, A275847.

Formula

a(0) = 0, and for n >= 1: if A276950(n) = 1, then a(n) = 1, otherwise a(n) = 1 + a(A266193(n)).
Other identities. For all n >= 0:
a(n) = A257679(A225901(n)) = A257679(A275847(n)) = A257679(A273667(n)).

A275848 Permutation of natural numbers: a(0) = 0, a(A255411(n)) = A153880(a(n)), a(A256450(n)) = A273670(n).

Original entry on oeis.org

0, 1, 3, 4, 2, 5, 7, 9, 10, 11, 13, 15, 8, 16, 17, 18, 12, 19, 6, 20, 21, 22, 14, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 57, 26, 58, 59, 61, 32, 63, 64, 65, 66, 67, 68, 69, 36, 70, 71, 73, 38, 75, 50, 76, 77, 79, 56, 81, 30, 82, 83, 85, 60, 87, 88, 89, 90, 91, 92, 93, 62, 94, 95, 96, 72, 97, 48
Offset: 0

Views

Author

Antti Karttunen, Aug 13 2016

Keywords

Links

Crossrefs

Inverse: A275847.
Cf. A153880, A255411, A256450, A257680, A257684, A273662, A273670.
Similar permutations: A273668 (a more recursed variant), A275845, A275846.

Formula

a(0) = 0; for n >= 1: if A257680(n) = 0 [when n is one of the terms of A255411] then a(n) = A153880(a(A257684(n))), otherwise [when n is one of the terms of A256450], a(n) = A273670(A273662(n)).

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

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Sep 22 2016

Keywords

Comments

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

Links

Crossrefs

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

Programs

Formula

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

Views

Author

Antti Karttunen, Aug 13 2016

Keywords

Links

Crossrefs

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

Formula

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.

A275846 Permutation of natural numbers: a(0) = 0, a(A255411(n)) = A153880(n), a(A256450(n)) = A273670(a(n)).

Original entry on oeis.org

0, 1, 3, 5, 2, 9, 4, 15, 7, 21, 11, 29, 6, 17, 41, 10, 8, 23, 12, 57, 16, 13, 14, 33, 18, 77, 22, 19, 20, 45, 25, 101, 31, 27, 28, 63, 35, 129, 43, 39, 40, 87, 47, 165, 59, 53, 55, 111, 24, 65, 213, 81, 26, 71, 75, 141, 34, 89, 269, 105, 30, 37, 95, 99, 32, 183, 36, 46, 113, 341, 38, 135, 48, 42, 51, 119, 50, 125, 44, 231, 49, 64, 143, 431, 54, 52
Offset: 0

Views

Author

Antti Karttunen, Aug 13 2016

Keywords

Links

Crossrefs

Inverse: A275845.
Cf. A153880, A255411, A256450, A257680, A257684, A273662, A273670.
Similar permutations: A273668 (a more recursed variant), A275847, A275848.

Formula

a(0) = 0; for n >= 1: if A257680(n) = 0 [when n is one of the terms of A255411] then a(n) = A153880(A257684(n)), otherwise [when n is one of the terms of A256450], a(n) = A273670(a(A273662(n))).

A276954 Inverse permutation to A276953.

Original entry on oeis.org

1, 3, 2, 4, 7, 6, 11, 5, 16, 22, 29, 8, 37, 12, 46, 56, 67, 79, 92, 106, 121, 137, 154, 10, 172, 17, 191, 211, 232, 9, 254, 23, 277, 301, 326, 30, 352, 38, 379, 407, 436, 466, 497, 529, 562, 596, 631, 13, 667, 47, 704, 742, 781, 18, 821, 57, 862, 904, 947, 68, 991, 80, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379, 1432, 93
Offset: 1

Views

Author

Antti Karttunen, Sep 22 2016

Keywords

Links

Crossrefs

Inverse: A276953.
Cf. A276949, A276951.
Related or similar permutations: A257504, A275847.

Programs

  • Scheme
    (define (A276954 n) (let ((col (A276951 n)) (row (A276949 n))) (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))

Formula

a(n) = (1/2) * ((c+r)^2 - r - 3*c + 2), where c = A276951(n), and r = A276949(n).
As a composition of other permutations:
a(n) = A257504(A275847(n)).

A276956 Inverse permutation to A276955.

Original entry on oeis.org

1, 2, 3, 6, 10, 4, 15, 5, 21, 28, 36, 9, 45, 14, 55, 66, 78, 91, 105, 120, 136, 153, 171, 7, 190, 20, 210, 231, 253, 8, 276, 27, 300, 325, 351, 35, 378, 44, 406, 435, 465, 496, 528, 561, 595, 630, 666, 13, 703, 54, 741, 780, 820, 19, 861, 65, 903, 946, 990, 77, 1035, 90, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485, 104
Offset: 1

Views

Author

Antti Karttunen, Sep 22 2016

Keywords

Links

Crossrefs

Inverse: A276955.
Cf. A276949, A276951.
Related permutations: A257506, A275847.

Programs

  • Scheme
    (define (A276956 n) (let ((row (A276951 n)) (col (A276949 n))) (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))

Formula

a(n) = (1/2) * ((c+r)^2 - r - 3*c + 2), where c = A276949(n), and r = A276951(n).
As a composition of other permutations:
a(n) = A257506(A275847(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

Views

Author

Antti Karttunen, Sep 22 2016

Keywords

Links

Crossrefs

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

Programs

Formula

If A276950(n) = 0, then a(n) = A255411(A266193(n)), otherwise a(n) = A256450(A273663(n)).
Showing 1-8 of 8 results.

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