A257730 -id:A257730 - cp's OEIS frontend

A257801 Permutation of natural numbers: a(1)=1; a(oddprime(n)) = lucky(1+a(n)), a(not_an_oddprime(n)) = unlucky(a(n-1)).

1, 2, 3, 4, 7, 5, 9, 6, 11, 8, 13, 14, 25, 10, 17, 12, 15, 19, 33, 20, 35, 16, 21, 24, 18, 22, 27, 45, 43, 28, 31, 47, 23, 29, 34, 26, 51, 30, 38, 59, 63, 57, 115, 39, 42, 61, 37, 32, 40, 46, 36, 66, 73, 41, 52, 78, 83, 76, 49, 146, 67, 53, 56, 81, 50, 44, 79, 54, 60, 48, 163, 86, 87, 95, 55, 68, 101, 107, 171, 98, 64

Offset: 1

Antti Karttunen, May 09 2015

nonn

Here lucky(n) = n-th lucky number = A000959(n), unlucky(n) = n-th unlucky number = A050505(n), oddprime(n) = n-th odd prime = A065091(n), not_an_oddprime(n) = n-th natural number which is not an odd prime = A065090(n).

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

Inverse: A257802.
Cf. A000959, A000720, A010051, A050505, A062298, A065090, A065091.
Related or similar permutations: A257726, A257727, A257730, A257731.

a(1) = 1; a(2) = 2; if A010051(n) = 1 [i.e., when n is an (odd) prime] then a(n) = A000959(1+a(A000720(n)-1)), otherwise a(n) = A050505(a(A062298(n))).
As a composition of other permutations:
a(n) = A257726(A257727(n)).
a(n) = A257731(A257730(n)).

A257727 Permutation of natural numbers: a(1) = 1, a(oddprime(n)) = 1 + 2a(n), a(not_an_oddprime(n)) = 2a(n-1).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 9, 14, 11, 16, 20, 24, 13, 18, 15, 28, 22, 32, 17, 40, 48, 26, 36, 30, 21, 56, 25, 44, 64, 34, 80, 96, 19, 52, 72, 60, 29, 42, 23, 112, 50, 88, 33, 128, 68, 160, 192, 38, 41, 104, 144, 120, 58, 84, 49, 46, 27, 224, 100, 176, 66, 256, 37, 136, 320, 384, 31, 76, 57, 82, 208, 288, 240, 116, 45

Offset: 1

Antti Karttunen, May 09 2015

nonn

Here oddprime(n) = n-th odd prime = A065091(n) = A000040(n+1), not_an_oddprime(n) = n-th natural number which is not an odd prime = A065090(n).

			For n=2, which is the second natural number >= 1 that is not an odd prime [2 = A065090(2)], we compute 2*a(1) = 2 = a(2).
For n=4, which is A065090(3), we compute 2*a(3-1) = 2*2 = 4.
For n=5, and 5 is the second odd prime [5 = A065091(2)], thus a(5) = 1 + 2*a(2) = 5.
For n=9, which is the sixth natural number >= 1 not an odd prime (9 = A065090(6)), we compute 2*a(6-1) = 2*5 = 10.
For n=11, which is the fourth odd prime [11 = A065091(4)], we compute 1 + 2*a(4) = 1 + 2*4 = 9, thus a(11) = 9.

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

Inverse: A257728.
Cf. A000720, A010051, A062298, A065090, A065091.
Related or similar permutations: A246377, A246378, A257725, A257730, A257801.

a(1) = 1; a(2) = 2; and for n > 2, if A010051(n) = 1 [i.e., when n is a prime], then a(n) = 1 + 2*a(A000720(n)-1), otherwise a(n) = 2*a(A062298(n)).
As a composition of other permutations:
a(n) = A246377(A257730(n)).
a(n) = A257725(A257801(n)).

A257729 Permutation of natural numbers: a(1)=1; a(prime(n)) = oddprime(a(n)), a(composite(n)) = not_an_oddprime(1+a(n)).

Original entry on oeis.org

1, 3, 7, 2, 19, 6, 5, 12, 4, 28, 71, 10, 17, 9, 20, 8, 13, 40, 41, 95, 16, 26, 11, 15, 30, 14, 21, 56, 109, 57, 359, 125, 25, 38, 18, 24, 31, 44, 22, 32, 61, 77, 29, 143, 78, 445, 73, 162, 36, 54, 27, 35, 23, 45, 62, 33, 46, 84, 43, 104, 179, 42, 185, 105, 545, 98, 181, 208, 51, 75, 503, 39, 59, 50, 34, 63, 85, 48, 103, 64, 114, 60, 37

Offset: 1

Antti Karttunen, May 09 2015

nonn

Here composite(n) = n-th composite = A002808(n), prime(n) = n-th prime = A000040(n), oddprime(n) = n-th odd prime = A065091(n) = A000040(n+1), not_an_oddprime(n) = n-th natural number which is not an odd prime = A065090(n).

			As an initial value we have a(1) = 1.
2 is the first prime (= A000040(1)), so we take the a(1)-th odd prime, A065091(1) = 3, thus a(2) = 3.
3 is the second prime, thus we take a(2)-th odd prime, A065091(3) = 7, thus a(3) = 7.
4 is the first composite, thus we take a(1)-th number larger than one which is not an odd prime, and that is A065090(1+1) = 2, thus a(4) = 2.
5 is the third prime, thus we take a(3)-th odd prime, which is A065091(7) = 19, thus a(5) = 19.

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

Inverse: A257730.
Cf. A000040, A002808, A000720, A010051, A065090, A065091, A065855.
Related or similar permutations: A257728, A246377, A257731, A257802, A236854.

A002808(n) = { my(k=-1); while( -n + n += -k + k=primepi(n), ); n};
A257729(n) = { if(1==n,n,if(isprime(n),prime(1+A257729(primepi(n))),if(4==n,2,A002808(A257729(n-primepi(n)-1)-1))))};
for(n=1, 10000, write("b257729.txt", n, " ", A257729(n)));
\\ After M. F. Hasler's PARI-code for A236854.

;; With memoizing definec-macro.
(definec (A257729 n) (cond ((<= n 1) n) ((= 1 (A010051 n)) (A065091 (A257729 (A000720 n)))) (else (A065090 (+ 1 (A257729 (A065855 n)))))))
;; Alternatively, by composing other permutations:
(define (A257729 n) (A257728 (A246377 n)))

a(1) = 1; if A010051(n) = 1 [i.e., if n is a prime], then a(n) = A065091(a(A000720(n))), otherwise a(n) = A065090(1+a(A065855(n))).
As a composition of other permutations:
a(n) = A257728(A246377(n)).
a(n) = A257802(A257731(n)).

A269847 Permutation of natural numbers: a(1) = 1, for n > 1, if n is an odd prime, a(n) = A003961(a(A000720(n))), otherwise a(n) = 2*a(n-A000720(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 9, 8, 10, 12, 7, 18, 15, 16, 20, 24, 25, 14, 27, 36, 30, 32, 21, 40, 48, 50, 28, 54, 45, 72, 11, 60, 64, 42, 80, 96, 75, 100, 56, 108, 35, 90, 81, 144, 22, 120, 63, 128, 84, 160, 192, 150, 135, 200, 112, 216, 70, 180, 49, 162, 33, 288, 44, 240, 126, 256, 125, 168, 320, 384, 225, 300, 105, 270, 400

Offset: 1

Antti Karttunen, Mar 06 2016

nonn

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

Inverse: A269848.
Cf. A000040, A000720, A003961, A005843, A007097, A010051, A026233, A065090, A065091.
Related or similar permutations: A071574, A163511, A246681, A257730, A269857.

a(1) = 1, and for n > 1, if n is an odd prime, a(n) = A003961(a(A000720(n))), otherwise [when n is 2 or composite] a(n) = 2*a(n-A000720(n)).
a(1) = 1; if n is an odd prime, a(n) = A003961(a(A026233(n))), else a(n) = A005843(a(A026233(n))).
Declarative definition:
a(1)=1, a(A065091(n)) = A003961(a(n+1)), a(A065090(n+1)) = 2*a(n).
As a composition of other permutations:
a(n) = A163511(A071574(n)).
Other identities. For all n >= 1:
a(A007097(n)) = A000040(n). [Maps the terms of primeth recurrence to primes.]

cp's OEIS Frontend

A257801 Permutation of natural numbers: a(1)=1; a(oddprime(n)) = lucky(1+a(n)), a(not_an_oddprime(n)) = unlucky(a(n-1)).

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A257727 Permutation of natural numbers: a(1) = 1, a(oddprime(n)) = 1 + 2a(n), a(not_an_oddprime(n)) = 2a(n-1).

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A257729 Permutation of natural numbers: a(1)=1; a(prime(n)) = oddprime(a(n)), a(composite(n)) = not_an_oddprime(1+a(n)).

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A269847 Permutation of natural numbers: a(1) = 1, for n > 1, if n is an odd prime, a(n) = A003961(a(A000720(n))), otherwise a(n) = 2*a(n-A000720(n)).

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cp's OEIS Frontend

A257801 Permutation of natural numbers: a(1)=1; a(oddprime(n)) = lucky(1+a(n)), a(not_an_oddprime(n)) = unlucky(a(n-1)).

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A257727 Permutation of natural numbers: a(1) = 1, a(oddprime(n)) = 1 + 2*a(n), a(not_an_oddprime(n)) = 2*a(n-1).

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A257729 Permutation of natural numbers: a(1)=1; a(prime(n)) = oddprime(a(n)), a(composite(n)) = not_an_oddprime(1+a(n)).

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A269847 Permutation of natural numbers: a(1) = 1, for n > 1, if n is an odd prime, a(n) = A003961(a(A000720(n))), otherwise a(n) = 2*a(n-A000720(n)).

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A257727 Permutation of natural numbers: a(1) = 1, a(oddprime(n)) = 1 + 2a(n), a(not_an_oddprime(n)) = 2a(n-1).