A267107 "Chebyshev's bat permutation": a(1) = 1, a(A080147(n)) = A080148(a(n)), a(A080148(n)) = A080147(a(n)).

1, 3, 2, 7, 6, 5, 4, 16, 13, 14, 12, 11, 9, 10, 35, 8, 29, 31, 30, 26, 23, 25, 21, 27, 22, 20, 24, 74, 17, 19, 18, 62, 67, 66, 15, 65, 54, 57, 51, 58, 55, 56, 45, 48, 43, 59, 50, 44, 53, 47, 39, 152, 49, 37, 41, 42, 38, 40, 46, 144, 130, 32, 139, 137, 36, 34, 33, 118, 136, 129, 128, 113, 121, 28, 108, 122, 125

Offset: 1

Author

Antti Karttunen, Feb 01 2016

Keywords

• nonn
• look

Comments

This is a self-inverse permutation of natural numbers.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001
• Antti Karttunen, Entanglement Permutations, 2016-2017.
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000040, A002144, A002145, A038698, A080147, A080148, A267097, A267098.

Cf. A268393 (record positions), A268394 (record values).

Cf. A267100, A267105, A267106 and also A270193, A270194, A270199, A270201, A270202 for other similarly constructed permutations based on prime distribution biases.

Programs

PARI

allocatemem(2^30);
default(primelimit,4294965247);
uplim = 2^20;
uplim2 = 366824; \\ Very ad hoc.
v080147 = vector(uplim);
v080148 = vector(uplim);
v267097 = vector(uplim);
v267107 = vector(uplim);
v267097[1] = 0; c = 0; v47i = 0; v48i = 0; for(n=2, uplim, if((1 == (prime(n)%4)), c++; v47i++; v080147[v47i] = n, v48i++; v080148[v48i] = n); v267097[n] = c; if(!(n%32768),print1(" n=",n)));
A080147(n) = v080147[n];
A080148(n) = v080148[n];
A267097(n) = v267097[n];
A267098(n) = (n - A267097(n))-1;
A267107(n) = v267107[n];
v267107[1] = 1; for(n=2, uplim2, if((1 == (prime(n) % 4)), v267107[n] = A080148(A267107(A267097(n))), v267107[n] = A080147(A267107(A267098(n))));  if(!(n%32768),print1(" n=",n)));
for(n=1, uplim2, write("b267107.txt", n, " ", A267107(n)));

Scheme

;; With memoization-macro definec
(definec (A267107 n) (cond ((<= n 1) n) ((= 1 (modulo (A000040 n) 4)) (A080148 (A267107 (A267097 n)))) (else (A080147 (A267107 (A267098 n))))))

Formula

a(1) = 1; and for n > 1, if prime(n) modulo 4 = 1, a(n) = A080148(a(A267097(n))), otherwise a(n) = A080147(a(A267098(n))).

Extensions

Name changed, the old name was "Manta moth permutation" - Antti Karttunen, Dec 10 2019