A269858 -id:A269858

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A269848

a(1) = 1, a(2n) = A065090(1+a(n)), a(2n+1) = A000040(a(A064989(2n+1))).

+10
4

1, 2, 3, 4, 5, 6, 11, 8, 7, 9, 31, 10, 127, 18, 13, 14, 709, 12, 5381, 15, 23, 45, 52711, 16, 17, 165, 19, 27, 648391, 21, 9737333, 22, 61, 856, 41, 20, 174440041, 6185, 197, 24, 3657500101, 34, 88362852307, 63, 29, 58644, 2428095424619, 25, 59, 26, 977, 212

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Term a(47) manually copied from A007097(15). Note that A000040(15) = 47.

LINKS

Table of n, a(n) for n=1..52.

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1) = 1, a(2) = 2, for n > 2, if n is even, a(n) = A002808(a(n/2)-1), and for odd n, a(n) = A000040(a(A064989(n))).

As a composition of other permutations:

a(n) = A237739(A243071(n)).

Other identities. For all n >= 1:

a(A000040(n)) = A007097(n). [Maps primes to the primeth recurrence.]

PROG

(PARI)

allocatemem(2^30);

default(primelimit, 4294965247);

A002808(n) = { my(k=-1); while( -n + n += -k + k=primepi(n), ); n}; \\ This function from M. F. Hasler

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};

A269848 = n -> if(n<=2, n, if((n%2), prime(A269848(A064989(n))), A002808(A269848(n/2)-1)));

for(n=1, 52, t = A269848(n); print1(t, ", "); write("b269848.txt", n, " ", t));

(Scheme, with memoization-macro definec)

(definec (A269848 n) (cond ((<= n 1) n) ((even? n) (A065090 (+ 1 (A269848 (/ n 2))))) (else (A000040 (A269848 (A064989 n))))))

CROSSREFS

Inverse: A269847.

Cf. A000040, A007097, A002808, A064989, A065090.

Related or similar permutations: A237739, A243071, A246682, A269858.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 06 2016

STATUS

approved

A269857

Permutation of natural numbers: a(1) = 1; if n is an odd prime, a(n) = A250469(a(A026233(n))), else a(n) = 2*(a(A026233(n))).

+10
3

1, 2, 3, 4, 5, 6, 9, 8, 10, 12, 7, 18, 15, 16, 20, 24, 25, 14, 21, 36, 30, 32, 27, 40, 48, 50, 28, 42, 33, 72, 11, 60, 64, 54, 80, 96, 51, 100, 56, 84, 35, 66, 45, 144, 22, 120, 57, 128, 108, 160, 192, 102, 69, 200, 112, 168, 70, 132, 49, 90, 39, 288, 44, 240, 114, 256, 55, 216, 320, 384, 105, 204, 87, 138, 400