A237739 a(0) = 1, a(2n) = nthcomposite(a(n)-1), a(2n+1) = nthprime(a(n)), where nthcomposite = A002808, nthprime = A000040.

1, 2, 4, 3, 8, 7, 6, 5, 14, 19, 12, 17, 10, 13, 9, 11, 22, 43, 28, 67, 20, 37, 26, 59, 16, 29, 21, 41, 15, 23, 18, 31, 33, 79, 60, 191, 40, 107, 91, 331, 30, 71, 52, 157, 38, 101, 81, 277, 25, 53, 42, 109, 32, 73, 57, 179, 24, 47, 34, 83, 27, 61, 45, 127, 48

Offset

0,2

Comments

A071574(a(n)) = n; a(A071574(n)) = n for n > 0.

Links

Reinhard Zumkeller (terms 0-300) & Antti Karttunen, Table of n, a(n) for n = 0..4095

Index entries for sequences that are permutations of the natural numbers

Formula

a(0) = 1, a(2n) = nthcomposite(a(n)-1), a(2n+1) = nthprime(a(n)), where nthcomposite = A002808, nthprime = A000040. - Antti Karttunen, Apr 04 2015

Prog

(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a237739 = fromIntegral . (+ 1) . fromJust . (`elemIndex` a071574_list)
(PARI)
default(primelimit, (2^31)+(2^30));
A002808(n) = { my(k=-1); while( -n + n += -k + k=primepi(n), ); n }; \\ This function from M. F. Hasler
A237739(n) = if(0==n, 1, if(!(n%2), A002808(A237739(n/2)-1), prime(A237739((n-1)/2))));
for(n=0, 4095, write("b237739.txt", n, " ", A237739(n)));
\\ Antti Karttunen, Apr 04 2015
(Scheme, with memoizing definec-macro)
(definec (A237739 n) (cond ((zero? n) 1) ((odd? n) (A000040 (A237739 (/ (- n 1) 2)))) (else (A002808 (+ -1 (A237739 (/ n 2)))))))
;; Antti Karttunen, Apr 04 2015

Crossrefs

Inverse: A071574.

Cf. A000040, A002808.

Compare also to the permutation A246378.

Sequence in context: A125566 A255833 A166133 * A337909 A358523 A365930

Adjacent sequences: A237736 A237737 A237738 * A237740 A237741 A237742

Keyword

nonn,look

Author

Reinhard Zumkeller, Apr 30 2014

Extensions

Name replaced by an explicit recurrence. - Antti Karttunen, Apr 04 2015

Status

approved