A390771 - OEIS

%I #32 Dec 07 2025 16:16:30

%S 22,33,35,37,57,77,313,513,317,319,519,323,523,723,329,331,531,731,

%T 337,537,341,343,543,347,547,747,353,553,753,359,361,561,761,367,567,

%U 371,373,573,773,379,579,383,583,783,389,589,789,1979,397,597,797,1789,1197

%N a(n) is the minimal concatenation pq of two primes p <= q such that p + q = 2*n.

%H Michael S. Branicky, <a href="/A390771/b390771.txt">Table of n, a(n) for n = 2..10001</a>

%H James S. DeArmon, <a href="/A390771/a390771.txt">R Code for A390771</a>

%e a(2) = 22 because 2+2 = 4.

%e a(3) = 33 because 3+3 = 6.

%e a(8) = 313 because 3+13 = 16.

%p a:= n-> min(seq((l-> `if`(andmap(isprime, l),

%p       parse(cat(l[])), [][]))([n-i, n+i]), i=0..n-2)):

%p seq(a(n), n=2..60);  # _Alois P. Heinz_, Nov 28 2025

%o (R) # See DeArmon link.

%o (Python)

%o from sympy import isprime, sieve

%o def a(n): return min(int(str(p)+str(q)) for p in sieve.primerange(3, n+1) if isprime(q:=2*n-p)) if n > 2 else 22

%o print([a(n) for n in range(2, 55)]) # _Michael S. Branicky_, Dec 01 2025

%Y Cf. A073046, A014091, A157931, A000040.

%K nonn,base

%O 2,1

%A _James S. DeArmon_, Nov 18 2025