A302854 Inverse of A302853: if A302853(k) = n, a(n) = k, or -1 if n does not occur in A302853.

0, 1, 3, 2, 5, 25, 4, 26, 7, 8, 10, 9, 6, 28, 11, 27, 13, 14, 16, 15, 18, 30, 17, 31, 20, 21, 23, 22, 19, 29, 12, 24, 65, 66, 7483, 7484, 70, 90, 7488, 7508, 68, 67, 7486, 7485, 69, 91, 7487, 7509, 72, 73, 7490, 7491, 71, 93, 7489, 7511, 75, 74, 7493, 7492, 76, 92, 7494, 7510, 33, 34, 36, 35, 38, 58, 37, 59, 40, 41, 43, 42, 39

Offset: 0

Author

Antti Karttunen, May 17 2018

Keywords

• nonn

Comments

This is a left inverse of A302853, and also the right inverse if A282291 (and thus also A302853) is surjective (a permutation of natural numbers), in which case the fallback-clause is unnecessary.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..259

Crossrefs

Cf. A302853 (inverse).

Programs

PARI

\\ For other needed code, follow A050376 and A282291:
A052330(n) = { my(p=1, i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
A302854(n) = (A304090(A052330(n))-1);

Formula

For all n >= 0, a(A302853(n)) = n.