cp's OEIS Frontend

A159296 a(n) is the smaller number in the pair (L,m) which minimizes the primes of the form L^2 + m^2 under the constraint L + m = 2n + 1.

%I A159296 #6 Aug 20 2017 23:17:58
%S A159296 1,2,2,4,5,5,7,7,9,8,10,12,10,14,11,14,17,15,19,18,20,22,22,24,25,25,
%T A159296 23,26,29,30,29,32,30,34,35,34,34,37,39,31,40,42,41,40,43,44,47,45,40,
%U A159296 50,50,47,51,52,53,55,54,56,55,60,59,61,62,55,65,65,64,66,69,70,64,72,67,72,65
%N A159296 a(n) is the smaller number in the pair (L,m) which minimizes the primes of the form L^2 + m^2 under the constraint L + m = 2n + 1.
%C A159296 1) It is known that this sequence is infinite.
%C A159296 2) L and m with odd sum L + m are necessarily coprime if L^2 + M^2 is prime.
%C A159296 3) The "singular" case m = L = 1, L + m = 2 (even) with 1^2 + 1^2 = 2 is skipped. It would define a(0)=1.
%C A159296 4) a(n) <= n.
%C A159296 It has not been proved that a(n) exists for all n. See A036468. [_T. D. Noe_, Apr 22 2009]
%e A159296 n=1: 1^2 + 2^2 = 5; a(1)=1.
%e A159296 n=2: 2^2 + 3^2 = 13 < 1^2 + 4^2 = 17; a(2)=2.
%e A159296 n=3: 2^2 + 5^2 = 29 < 1^2 + 6^2 = 37. 3^2 + 4^2 = 5^2 not prime; a(3)=2.
%e A159296 n=27: 23^2 + 32^2 = 1553 < 1597, 1657, 1693, 1733, 1777, 1877, 1933, 1993, 2273, 2437, 2617, 2713, 2917, a(27)=23.
%p A159296 A159296 := proc(n) local a,pmin,l,m ; a := 0 ; pmin := 2*(2*n+1)^2 ; for l from 1 to n do m := 2*n+1-l ; if isprime(m^2+l^2) then if m^2+l^2 < pmin then pmin := m^2+l^2 ; a := l ; fi; fi; od: RETURN(a) ; end: seq(A159296(n),n=1..80) ; # _R. J. Mathar_, Apr 18 2009
%Y A159296 Cf. A145354, A157884.
%K A159296 easy,nonn
%O A159296 1,2
%A A159296 Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 09 2009
%E A159296 Edited and extended by _R. J. Mathar_, Apr 18 2009