A256486 -id:A256486 - cp's OEIS frontend

A256487 a(n) = A254100(n) - A219178(n).

2, 4, 0, 4, 10, 18, 16, 36, 28, 48, 78, 80, 62, 90, 76, 110, 134, 158, 200, 220, 224, 216, 236, 280, 308, 312, 262, 314, 328, 402, 430, 424, 438, 488, 506, 538, 414, 510, 642, 620, 680, 648, 656, 690, 666, 684, 730, 790, 742, 840, 844, 862, 916, 976, 1004, 1092, 1072, 1112, 1054, 1166, 1176, 1184, 1292

Offset: 1

Antti Karttunen, May 01 2015

nonn

Difference between the least nonludic number removed at the n-th stage of Ludic sieve and the least unlucky number removed at the n-th stage of Lucky sieve.

Antti Karttunen, Table of n, a(n) for n = 1..933
Index entries for sequences generated by sieves

Cf. A219178, A254100, A256482, A256486, A256488 (same terms divided by 2).

(define (A256487 n) (- (A254100 n) (A219178 n)))

a(n) = A254100(n) - A219178(n).

A257733 Permutation of natural numbers: a(1) = 1, a(ludic(n)) = lucky(1+a(n-1)), a(nonludic(n)) = unlucky(a(n)), where ludic(n) = n-th ludic number A003309, nonludic(n) = n-th nonludic number A192607 and lucky = A000959, unlucky = A050505.

Original entry on oeis.org

1, 3, 9, 2, 33, 5, 7, 14, 4, 45, 163, 8, 15, 11, 20, 6, 25, 59, 203, 12, 22, 17, 63, 28, 13, 10, 35, 78, 235, 251, 18, 30, 24, 83, 39, 19, 1093, 16, 47, 101, 31, 290, 67, 309, 26, 41, 43, 34, 107, 53, 27, 1283, 87, 23, 61, 128, 42, 354, 88, 376, 21, 36, 55, 57, 46, 137, 115, 70, 38, 1499, 321, 112, 32, 81, 161, 56, 1401, 430, 113, 454, 29, 48, 49

Offset: 1

Antti Karttunen, May 06 2015

Antti Karttunen, Table of n, a(n) for n = 1..8587
Index entries for sequences that are permutations of the natural numbers

Inverse: A257734.
Cf. A000959, A050505, A003309, A192607, A192490, A192512, A236863.
Related or similar permutations: A237427, A255422, A257726, A257731.
Cf. also A256486, A256487.
Differs from A257731 for the first time at n=19, where a(19) = 203, while A257731(19) = 63.

a(1) = 1; for n > 1: if A192490(n) = 1 [i.e., if n is ludic], then a(n) = A000959(1+a(A192512(n)-1)), otherwise a(n) = A050505(a(A236863(n))).
As a composition of other permutations:
a(n) = A257731(A255422(n)).
a(n) = A257726(A237427(n)).

A257734 Permutation of natural numbers: a(1) = 1, a(lucky(n)) = ludic(1+a(n-1)), a(unlucky(n)) = nonludic(a(n)), where lucky(n) = n-th lucky number A000959, unlucky(n) = n-th unlucky number A050505, and ludic = A003309, nonludic = A192607.

Original entry on oeis.org

1, 4, 2, 9, 6, 16, 7, 12, 3, 26, 14, 20, 25, 8, 13, 38, 22, 31, 36, 15, 61, 21, 54, 33, 17, 45, 51, 24, 81, 32, 41, 73, 5, 48, 27, 62, 119, 69, 35, 105, 46, 57, 47, 96, 10, 65, 39, 82, 83, 151, 115, 92, 50, 135, 63, 76, 64, 124, 18, 86, 55, 106, 23, 108, 189, 146, 43, 118, 193, 68, 169, 84, 91, 100, 149, 85, 156, 28, 179, 111, 74, 136, 34

Offset: 1

Antti Karttunen, May 06 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Inverse: A257733.
Cf. A000959, A050505, A003309, A109497, A145649, A192607.
Related or similar permutations: A237126, A255421, A257725, A257732.
Cf. also A256486, A256487.

a(1) = 1; for n > 1: if A145649(n) = 1 [i.e., if n is lucky], then a(n) = A003309(1+a(A109497(n)-1)), otherwise a(n) = A192607(a(n-A109497(n))).
As a composition of other permutations:
a(n) = A255421(A257732(n)).
a(n) = A237126(A257725(n)).

A256483 a(n) = A256482(n)/2 = (A254100(n) - A003309(n+1)) / 2.

Original entry on oeis.org

1, 3, 7, 12, 22, 30, 42, 61, 71, 88, 108, 126, 137, 154, 180, 206, 227, 249, 273, 297, 324, 336, 368, 405, 434, 454, 465, 497, 520, 565, 594, 627, 655, 699, 722, 742, 750, 807, 874, 890, 933, 945, 972, 1006, 1020, 1048, 1077, 1120, 1164, 1218, 1244, 1272, 1338, 1370, 1400, 1474, 1488, 1517, 1545, 1605, 1627

Offset: 1

Antti Karttunen, May 01 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..4096

Column 1 of A257258.
Cf. A003309, A254100, A256482.
Cf. also A256486, A256487.

Scheme
```
(define (A256483 n) (/ (A256482 n) 2))
```

a(n) = A256482(n)/2 = (A254100(n) - A003309(n+1)) / 2.

A256488 a(n) = A256487(n)/2 = (A254100(n) - A219178(n))/2.

Original entry on oeis.org

1, 2, 0, 2, 5, 9, 8, 18, 14, 24, 39, 40, 31, 45, 38, 55, 67, 79, 100, 110, 112, 108, 118, 140, 154, 156, 131, 157, 164, 201, 215, 212, 219, 244, 253, 269, 207, 255, 321, 310, 340, 324, 328, 345, 333, 342, 365, 395, 371, 420, 422, 431, 458, 488, 502, 546, 536, 556, 527, 583, 588, 592, 646, 643, 639, 665, 688, 662, 662

Offset: 1

Antti Karttunen, May 01 2015

nonn

Half the difference between the least nonludic number removed at the n-th stage of Ludic sieve and the least unlucky number removed at the n-th stage of Lucky sieve.

Antti Karttunen, Table of n, a(n) for n = 1..933

Cf. A219178, A254100, A256482, A256486, A256487.

Scheme
```
(define (A256488 n) (/ (A256487 n) 2))
```

a(n) = A256487(n)/2 = (A254100(n) - A219178(n))/2.

A260722 Difference between n-th odd Ludic and n-th Lucky number: a(1) = 0; for n > 1: a(n) = A003309(n+1) - A000959(n).

Original entry on oeis.org

0, 0, -2, -2, -2, -2, -4, -2, -6, -4, 0, -2, -6, -4, -10, -6, -2, -2, 2, 4, 2, -2, -2, 2, 4, 4, -6, -2, -2, 8, 8, 6, 2, 10, 6, 8, -8, 0, 14, 10, 16, 12, 8, 10, 4, 4, 10, 16, 6, 16, 16, 14, 18, 22, 24, 32, 28, 30, 22, 32, 32, 30, 38, 34, 32, 36, 40, 30, 28, 28, 32, 24, 22, 24, 36, 38, 42, 30, 30, 22, 26, 26, 30, 38, 40, 30, 36, 46, 48, 46, 56, 54, 54, 54, 40, 46

Offset: 1

Antti Karttunen, Aug 06 2015

sign

Equally: for n >= 2, the difference between (n+1)-th Ludic and n-th Lucky number.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences generated by sieves

Cf. A000959, A003309, A031883, A260721 (same terms divided by two), A260723, A256486, A256487.

Cf. also permutations A260435, A260436, A260741, A260742.

(define (A260722 n) (if (= 1 n) 0 (- (A003309 (+ 1 n)) (A000959 n))))

a(1) = 0; for n > 1: a(n) = A003309(n+1) - A000959(n).
Other identities. For all n >= 2:
a(n) = A256486(n) + A260723(n).
a(n) = A256486(n+1) + A031883(n).

cp's OEIS Frontend

A256487 a(n) = A254100(n) - A219178(n).

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A257733 Permutation of natural numbers: a(1) = 1, a(ludic(n)) = lucky(1+a(n-1)), a(nonludic(n)) = unlucky(a(n)), where ludic(n) = n-th ludic number A003309, nonludic(n) = n-th nonludic number A192607 and lucky = A000959, unlucky = A050505.

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A257734 Permutation of natural numbers: a(1) = 1, a(lucky(n)) = ludic(1+a(n-1)), a(unlucky(n)) = nonludic(a(n)), where lucky(n) = n-th lucky number A000959, unlucky(n) = n-th unlucky number A050505, and ludic = A003309, nonludic = A192607.

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Formula

A256483 a(n) = A256482(n)/2 = (A254100(n) - A003309(n+1)) / 2.

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Scheme

Formula

A256488 a(n) = A256487(n)/2 = (A254100(n) - A219178(n))/2.

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Programs

Scheme

Formula

A260722 Difference between n-th odd Ludic and n-th Lucky number: a(1) = 0; for n > 1: a(n) = A003309(n+1) - A000959(n).

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Formula