A135761 -id:A135761 - cp's OEIS frontend

A135762 Start with sequence of positive integers, then swap a(i) and a(i-1) if a(i) is an odd prime.

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

Offset: 1

Zak Seidov, Nov 27 2007

nonn

			a(1)=1; then
a(2)=3 and a(3)=2 because p=3 is odd prime and p and p-1 are swapped.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A135761.

r=Range[100];Do[If[PrimeQ[r[[i]]],{r[[i]],r[[i-1]]}={r[[i-1]],r[[i]]}],{i,3,97,2}];r

A181097 Permutation of positive integers created from sequence A002808(n) = composites.

Original entry on oeis.org

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

Offset: 1

Jaroslav Krizek, Oct 02 2010

nonn

Method of creation of sequence a(n) from b(n) = A002808(n):
Take b(1) and put in vacancy place a(1), swap this place and b(1), repeat with b(2), b(3), ...:
b(1) = 4, a(1) = 4, a(4) = 1,
b(2) = 6, a(2) = 6, a(6) = 2,
b(3) = 8, a(3) = 8, a(8) = 3,
b(4) = 9, a(5) = 9, a(9) = 5,
b(5) = 10, a(7) = 10, a(10) = 7,
...

a(n) = A135761(n) for n >= 11. a(n) = A181096(n) for n >= 11.

A181096 Permutation of positive integers created from sequence A018252(n) = nonprimes.

Original entry on oeis.org

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

Offset: 1

Jaroslav Krizek, Oct 02 2010

nonn

Method of creation of sequence a(n) from b(n) = A018252(n):
Take b(1) and put in vacancy place a(1), swap this place and b(1), repeat with b(2), b(3), ...:
b(1) = 1, a(1) = 1,
b(2) = 4, a(2) = 4, a(4) = 2,
b(3) = 6, a(3) = 6, a(6) = 3,
b(4) = 8, a(5) = 8, a(8) = 5,
b(5) = 9, a(7) = 9, a(9) = 7,
...

a(n) = A135761(n) for n >= 11. a(n) = A181097(n) for n >= 11.

cp's OEIS Frontend

A135762 Start with sequence of positive integers, then swap a(i) and a(i-1) if a(i) is an odd prime.

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A181097 Permutation of positive integers created from sequence A002808(n) = composites.

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A181096 Permutation of positive integers created from sequence A018252(n) = nonprimes.

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