A332211 Lexicographically earliest permutation of primes such that a(n) = 2^n - 1 when n is one of the Mersenne prime exponents (in A000043).

2, 3, 7, 5, 31, 11, 127, 13, 17, 19, 23, 29, 8191, 37, 41, 43, 131071, 47, 524287, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 2147483647, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 2305843009213693951, 269, 271, 277, 281, 283, 293, 307, 311, 313

Offset

1,1

Comments

Sequence is well-defined also in case there are only a finite number of Mersenne primes.

Links

Antti Karttunen, Table of n, a(n) for n = 1..3217

Formula

For all applicable n >= 1, a(A000043(n)) = A000668(n).

Example

For p in A000043: 2, 3, 5, 7, 13, 17, 19, ..., a(p) = (2^p)-1, thus a(2) = 2^2 - 1 = 3, a(3) = 7, a(5) = 31, a(7) = 127, a(13) = 8191, a(17) = 131071, etc., with the rest of positions filled by the least unused prime:
1, 2, 3, 4,  5,  6,   7,  8,  9, 10, 11, 12,   13, 14, 15, 16, 17, ...
2, 3, 7, 5, 31, 11, 127, 13, 17, 19, 23, 29, 8191, 37, 41, 43, 131071, ...

Prog

(PARI)
up_to = 127;
A332211list(up_to) = { my(v=vector(up_to), xs=Map(), i=1, q); for(n=1, up_to, if(isprime(q=((2^n)-1)), v[n] = q, while(mapisdefined(xs, prime(i)), i++); v[n] = prime(i)); mapput(xs, v[n], n)); (v); };
v332211 = A332211list(up_to);
A332211(n) = v332211[n];
\\ For faster computing of larger values, use precomputed values of A000043:
v000043 = [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217];
up_to = v000043[#v000043];
A332211list(up_to) = { my(v=vector(up_to), xs=Map(), i=1, q); for(n=1, up_to, if(vecsearch(v000043, n), q = (2^n)-1, while(mapisdefined(xs, prime(i)), i++); q = prime(i)); v[n] = q; mapput(xs, q, n)); (v); };

Crossrefs

Cf. A000040, A000043, A000668, A332210 (inverse permutation of primes), A332220.

Used to construct permutations A332212, A332214.

Sequence in context: A085399 A063696 A258126 * A353075 A069587 A059843

Adjacent sequences: A332208 A332209 A332210 * A332212 A332213 A332214

Keyword

nonn

Author

Antti Karttunen, Feb 09 2020

Status

approved