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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.
5
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 02 2021
STATUS
approved