A255407 -id:A255407 - cp's OEIS frontend

A255415 Row 5 of Ludic array A255127.

11, 55, 103, 151, 203, 251, 299, 343, 391, 443, 491, 539, 587, 631, 683, 731, 779, 827, 877, 923, 971, 1019, 1067, 1117, 1165, 1211, 1259, 1307, 1357, 1405, 1453, 1499, 1547, 1597, 1645, 1693, 1741, 1787, 1837, 1885, 1933, 1981, 2033, 2077, 2125, 2173, 2221, 2273, 2321, 2365, 2413, 2461, 2513, 2561, 2609, 2653, 2701, 2753, 2801, 2849, 2897, 2941, 2993, 3041

Offset: 1

Antti Karttunen, Feb 22 2015

nonn

First differences are periodic with period length 48, cf. formulas. - M. F. Hasler, Nov 17 2024

Antti Karttunen, Table of n, a(n) for n = 1..10001

Row 5 of A255127. See A255414 for row 4 and A255416 for row 6.

Cf. A084969, A255407.

L255415=[n*337\14*2+7|n<-[0..47]]+digits(54129937554927109457534, 3)*2
apply( A255415(n)=n--\48*2310+L255415[n%48+1], [1..66]) \\ M. F. Hasler, Nov 10 2024

(define (A255415 n) (A255127bi 5 n)) ;; Code for A255127bi given in A255127.

a(n) = A255407(A084969(n)).

a(n) = a(n-48) + 2310 = a((n-1)%48 + 1) + [(n-1)/48]*2310, where % = mod = remainder operator, and [.] = floor. - M. F. Hasler, Nov 10 2024

A260435 Permutation mapping from Lucky sieve to Ludic sieve: a(1) = 1, for n > 1: a(n) = A255127(A260438(n), A260439(n)).

Original entry on oeis.org

1, 2, 3, 4, 9, 6, 5, 8, 7, 10, 15, 12, 11, 14, 13, 16, 21, 18, 19, 20, 17, 22, 27, 24, 23, 26, 31, 28, 33, 30, 25, 32, 29, 34, 39, 36, 37, 38, 35, 40, 45, 42, 41, 44, 55, 46, 51, 48, 43, 50, 47, 52, 57, 54, 73, 56, 59, 58, 63, 60, 49, 62, 53, 64, 69, 66, 61, 68, 67, 70, 75, 72, 71, 74, 77, 76, 81, 78, 83, 80, 65, 82, 87, 84, 101, 86, 89, 88

Offset: 1

Antti Karttunen, Jul 30 2015

nonn

a(n) tells which number in array A255127 (constructed from Ludic sieve) is at the same position where n is in array A255551 (constructed from Lucky sieve). This permutation fixes all even numbers because both arrays have A005843 as their topmost row.

Inverse: A260436.
Cf. A000959, A003309, A255127, A260438, A260439.
Similar or related permutations: A255407, A255552, A255554, A249817, A249818, A260741 (a more recursed variant).

(define (A260435 n) (if (<= n 1) n (A255127bi (A260438 n) (A260439 n)))) ;; Code for A255127bi given in A255127.

Other identities. For all n >= 1:
a(A000959(n+1)) = A003309(n+2). [Maps Lucky numbers to odd Ludic numbers.]
a(2n) = 2n.
As a composition of related permutations:
a(n) = A255127(A255552(n)).
a(n) = A255407(A255554(n)).

A269355 Permutation of natural numbers: a(n) = A269380(A250469(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 23, 10, 11, 12, 13, 14, 15, 16, 9, 18, 17, 20, 31, 22, 25, 24, 21, 26, 27, 28, 19, 30, 29, 32, 49, 34, 71, 36, 37, 38, 39, 40, 41, 42, 43, 44, 107, 46, 47, 48, 119, 50, 51, 52, 35, 54, 89, 56, 101, 58, 53, 60, 61, 62, 63, 64, 115, 66, 67, 68, 173, 70, 55, 72, 33, 74, 75, 76, 131, 78, 77, 80, 167

Offset: 1

Antti Karttunen, Mar 03 2016

nonn

			For n=9 we first find what number is below 9 in square array A083221, which is 25, then we find what number is above 25 in square array A255127, which is 23, thus a(9) = 23.

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

Inverse: A269356.
Cf. A250469, A269380.
Cf. also arrays A083221 & A255127.
More recursed variant: A269357. Cf. also permutations A266645, A255407, A269171.

(define (A269355 n) (A269380 (A250469 n)))

a(n) = A269380(A250469(n)).
Other identities. For all n >= 1:
a(2n) = 2n. [Fixes the even numbers.]

A255410 Main diagonal of Ludic array A255127 (and A255129): a(n) = A255127(n,n).

Original entry on oeis.org

2, 9, 35, 85, 203, 325, 547, 911, 1181, 1591, 2347, 2923, 3421, 4151, 5161, 6461, 7693, 8785, 10237, 11789, 13469, 14621, 16523, 19225, 21775, 23669, 25237, 27715, 29891, 34073, 36977, 40487, 43151, 48091, 50429, 53407, 55843, 61541, 68797, 71603, 77279, 80291, 84091, 88771, 91997, 96119, 101927, 108833, 115031, 123187

Offset: 1

Antti Karttunen, Feb 22 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..1024

Cf. A083141, A255127, A255129, A255407.

(define (A255410 n) (A255127bi n n)) ;; Code for A255127bi given in A255127.

a(n) = A255127(n,n).

a(n) = A255407(A083141(n)).

A255416 Row 6 of Ludic array A255127.

Original entry on oeis.org

13, 73, 133, 197, 263, 325, 385, 449, 511, 571, 641, 701, 761, 823, 887, 947, 1013, 1075, 1139, 1199, 1261, 1327, 1387, 1447, 1513, 1573, 1637, 1703, 1763, 1825, 1889, 1951, 2011, 2071, 2141, 2201, 2261, 2327, 2387, 2453, 2515, 2575, 2639, 2699, 2767, 2827, 2887, 2953, 3013, 3073, 3143, 3203, 3265, 3325, 3389, 3451, 3511, 3581, 3641, 3701

Offset: 1

Antti Karttunen, Feb 22 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10001

Row 6 of A255127. See A255415 for row 5 and A255417 for row 7.

Cf. A084970, A255407.

my(L=[x+2^(x%2)|x<-[1..10^4]*3], m(n,k)=2^(n\/k*k)\(2^k-1)); for(i=3, 5, L=vecextract(L, 2^#L-m(#L, L[1])-1)); L255416=vecextract(L, m(#L, L[1]));
A255416(n)=n--\480*30030+L255416[n%480+1] \\ M. F. Hasler, Nov 17 2024

def A255416(n):
    try: n-=1; return A255416.L[n]
    except IndexError: return n//480*30030 + A255416.L[n%480]
    except AttributeError: L = [3*x+5-(x&1) for x in range(10**4)]
    for k in L[:3]: L = [x for i,x in enumerate(L) if i%k]
    A255416.L = L[::13]; return n//480*30030 + A255416.L[n%480]
# M. F. Hasler, Nov 17 2024

(define (A255416 n) (A255127bi 6 n)) ;; Code for A255127bi given in A255127.

a(n) = A255407(A084970(n)).

a(n) = a(n-480) + 30030 = 30030*floor((n-1)/480) + a((n-1)%480 + 1), where % is the modulo or remainder operator. - M. F. Hasler, Nov 10 2024 and Nov 17 2024

A269395 Permutation of natural numbers: a(n) = A269171(A269393(n)) = A269171(A269171(3*n)/3).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Mar 03 2016

nonn

Composition of A269171 with a permutation of natural numbers obtained from its trisection.

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Inverse: A269396.
Cf. A269393.
Differs from A255407 and A269171 for the first time at n=37, which here a(37)=45, instead of 41.

(define (A269395 n) (A269171 (A269393 n)))

a(n) = A269171(A269393(n)) = A269171(A269171(3*n)/3).

cp's OEIS Frontend

A255415 Row 5 of Ludic array A255127.

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A260435 Permutation mapping from Lucky sieve to Ludic sieve: a(1) = 1, for n > 1: a(n) = A255127(A260438(n), A260439(n)).

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A269355 Permutation of natural numbers: a(n) = A269380(A250469(n)).

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A255410 Main diagonal of Ludic array A255127 (and A255129): a(n) = A255127(n,n).

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A255416 Row 6 of Ludic array A255127.

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A269395 Permutation of natural numbers: a(n) = A269171(A269393(n)) = A269171(A269171(3*n)/3).

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