A322863 Permutation of natural numbers: a(0) = 1; for n >= 1, a(n) = A005940(1+A122111(n)).

1, 2, 3, 5, 4, 7, 9, 11, 6, 10, 25, 13, 15, 17, 49, 21, 8, 19, 16, 23, 35, 55, 121, 29, 27, 36, 169, 50, 77, 31, 81, 37, 12, 91, 289, 225, 30, 41, 361, 187, 125, 43, 625, 47, 143, 147, 529, 53, 45, 154, 90, 247, 221, 59, 28, 1225, 343, 391, 841, 61, 105, 67, 961, 605, 18, 5929, 2401, 71, 323, 551, 525, 73, 22, 79, 1369, 84, 437, 429, 14641, 83

Offset: 0

Author

Antti Karttunen, Dec 30 2018

Keywords

• nonn

Comments

Note the indexing: the domain starts from 0, but the range excludes zero.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Inverse permutation: A322864.

Cf. A005940, A122111, A322866, A322867.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
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)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A322863(n) = if(!n,1,A005940(1+A122111(n)));

Formula

a(0) = 1; for n >= 1, a(n) = A005940(1+A122111(n)).

For all n >= 1:

a(prime(n)) = prime(1+n).

A001222(a(n)) = A322867(n).