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

Author

Antti Karttunen, Nov 02 2021

Keywords

• nonn

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.

Crossrefs

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

Cf. also A108546, A332211.

Programs

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];

Formula

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