A269858 -id:A269858 - cp's OEIS frontend

A269848 a(1) = 1, a(2n) = A065090(1+a(n)), a(2n+1) = A000040(a(A064989(2n+1))).

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

Offset: 1

Antti Karttunen, Mar 06 2016

nonn

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

Index entries for sequences that are permutations of the natural numbers

Inverse: A269847.
Cf. A000040, A007097, A002808, A064989, A065090.
Related or similar permutations: A237739, A243071, A246682, A269858.

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));

;; With memoization-macro definec.
(definec (A269848 n) (cond ((<= n 1) n) ((even? n) (A065090 (+ 1 (A269848 (/ n 2))))) (else (A000040 (A269848 (A064989 n))))))

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.]

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))).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Mar 06 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..2662
Index entries for sequences that are permutations of the natural numbers

Inverse: A269858.
Cf. A005843, A026233, A010051, A250469.
Related or similar permutations: A071574, A252755, A269847.
Differs from A269847 for the first time at n=19, where a(19)=21, while A269847(19)=27.

a(1) = 1; if n is an odd prime, a(n) = A250469(a(A026233(n))), else a(n) = 2*(a(A026233(n))).
As a composition of other permutations:
a(n) = A252755(A071574(n)).

cp's OEIS Frontend

A269848 a(1) = 1, a(2n) = A065090(1+a(n)), a(2n+1) = A000040(a(A064989(2n+1))).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Scheme

Formula