A348744 Lexicographically earliest bijection from primes to odd primes where each prime of the form 4k+1 is mapped to the next larger prime that is of the same form.

3, 5, 13, 7, 11, 17, 29, 19, 23, 37, 31, 41, 53, 43, 47, 61, 59, 73, 67, 71, 89, 79, 83, 97, 101, 109, 103, 107, 113, 137, 127, 131, 149, 139, 157, 151, 173, 163, 167, 181, 179, 193, 191, 197, 229, 199, 211, 223, 227, 233, 241, 239, 257, 251, 269, 263, 277, 271, 281, 293, 283, 313, 307, 311, 317, 337, 331, 349, 347

Offset

1,1

Comments

Terms of A002144 map each to the next term there, as: 5 -> 13 -> 17 -> 29 -> 37 -> 41, etc., and the remaining positions are filled with the terms of A002145: 3, 7, 11, 19, 23, 31, 43, etc., which gives the result that 2 is mapped to 3, 3 is mapped 5, and the rest of 4k+3 primes are fixed.

Links

Table of n, a(n) for n=1..69.

Formula

a(n) = A348746(A000040(n)).

Prog

(PARI)
up_to = 10000;
A348744list(up_to) = { my(v=vector(up_to), xs=Map(), i=2, p, q); mapput(xs, v[1]=3, 1); for(n=2, up_to, p = prime(n); if(1==(p%4), for(k=1+n, oo, q=prime(k); if((1==(q%4))&&!mapisdefined(xs, q), v[n]=q; break)), while(mapisdefined(xs, prime(i)), i++); v[n] = prime(i)); mapput(xs, v[n], n)); (v); };
v348744 = A348744list(up_to);
A348744(n) = v348744[n];

Crossrefs

Cf. A000040, A002144, A002145, A348745, A348746.

Cf. also A108546, A332211.

Sequence in context: A099791 A301901 A351225 * A263829 A028268 A369901

Adjacent sequences: A348741 A348742 A348743 * A348745 A348746 A348747

Keyword

nonn

Author

Antti Karttunen, Nov 02 2021

Status

approved