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

Author

Antti Karttunen, Feb 09 2020

Keywords

• nonn

Comments

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

Examples

			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, ...
		

Links

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

Crossrefs

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

Used to construct permutations A332212, A332214.

Programs

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); };

Formula

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