A255421 - OEIS

A255421

Permutation of natural numbers: a(1) = 1, a(p_n) = ludic(1+a(n)), a(c_n) = nonludic(a(n)), where p_n = n-th prime, c_n = n-th composite number and ludic = A003309, nonludic = A192607.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 19, 20, 21, 25, 22, 24, 26, 27, 28, 29, 34, 37, 30, 31, 32, 36, 33, 41, 35, 38, 39, 43, 40, 47, 42, 49, 52, 53, 44, 45, 46, 51, 48, 61, 57, 50, 54, 55, 59, 67, 56, 71, 64, 58, 66, 70, 72, 97, 60, 62, 63, 77, 69, 83, 65, 81

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

OFFSET

1,2

COMMENTS

This can be viewed as yet another "entanglement permutation", where two pairs of complementary subsets of natural numbers are interwoven with each other. In this case a complementary pair ludic/nonludic numbers (A003309/A192607) is intertwined with a complementary pair prime/composite numbers (A000040/A002808).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1) = 1, and for n > 1, if A010051(n) = 1 [i.e. when n is a prime], a(n) = A003309(1+a(A000720(n))), otherwise a(n) = A192607(a(A065855(n))).

As a composition of other permutations:

a(n) = A237126(A246377(n)).

Other identities.

a(A007097(n)) = A255420(n). [Maps iterates of primes to the iterates of Ludic numbers.]

EXAMPLE

When n = 19 = A000040(8) [the eighth prime], we look for the value of a(8), which is 8 [all terms less than 19 are fixed because the beginnings of A003309 and A008578 coincide up to A003309(8) = A008578(8) = 17], and then take the eighth ludic number larger than 1, which is A003309(1+8) = 23, thus a(19) = 23.

When n = 20 = A002808(11) [the eleventh composite], we look for the value of a(11), which is 11 [all terms less than 19 are fixed, see above], and then take the eleventh nonludic number, which is A192607(11) = 19, thus a(20) = 19.

When n = 30 = A002808(19) [the 19th composite], we look for the value of a(19), which is 23 [see above], and then take the 23rd nonludic number, which is A192607(23) = 34, thus a(30) = 34.

PROG

(Scheme, with memoization-macro definec)

(definec (A255421 n) (cond ((= 1 n) n) ((= 1 (A010051 n)) (A003309 (+ 1 (A255421 (A000720 n))))) (else (A192607 (A255421 (A065855 n))))))

;; Alternatively:

(define (A255421 n) (A237126 (A246377 n)))

CROSSREFS

Inverse: A255422.

Cf. A000040, A000720, A002808, A003309, A007097, A008578, A065855, A010051, A192607, A255420, A255324.

Related or similar permutations: A237126, A246377, A245703, A245704, A255407, A255408.

Sequence in context: A194417 A246093 A261924 * A255407 A269171 A269395

Adjacent sequences: A255418 A255419 A255420 * A255422 A255423 A255424

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 23 2015

STATUS

approved