A348744 - OEIS

%I #8 Nov 02 2021 20:59:30

%S 3,5,13,7,11,17,29,19,23,37,31,41,53,43,47,61,59,73,67,71,89,79,83,97,

%T 101,109,103,107,113,137,127,131,149,139,157,151,173,163,167,181,179,

%U 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

%N 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.

%C 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.

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

%o (PARI)

%o up_to = 10000;

%o 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); };

%o v348744 = A348744list(up_to);

%o A348744(n) = v348744[n];

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

%Y Cf. also A108546, A332211.

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 02 2021