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A145354 It is conjectured that for each m >= 1 there exist primes Q=Q(m) and P=P(m) with (2m)^2 + 1 <= Q <= (2m+1)^2 - 2m <= P <= (2m+1)^2; then set a(2m-1) = Q, a(2m) = P. 7

%I #2 Mar 30 2012 17:39:44

%S 5,7,17,23,37,43,67,73,101,113,149,157,197,211,257,277,331,347,401,

%T 421,487,509,577,601,677,709,787,821,907,937,1031,1061,1163,1193,1297,

%U 1361,1447,1483,1601,1657,1777,1811,1949,1987,2129,2179,2309,2357,2503,2551

%N It is conjectured that for each m >= 1 there exist primes Q=Q(m) and P=P(m) with (2m)^2 + 1 <= Q <= (2m+1)^2 - 2m <= P <= (2m+1)^2; then set a(2m-1) = Q, a(2m) = P.

%C If there is more than one choice for Q or P we take the smallest.

%e m=1: 5 <= Q <= 7 <= P <= 9; this gives Q(1)= 5 and P(1)=7 => a(1)=5, a(2)=7

%e m=2: 17 <= Q <= 21 <= P <= 25; this gives smallest prime in the interval Q(2)= 17 and P(2)=23 => a(3)=17, a(4)=23

%K nonn

%O 1,1

%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 03 2009

%E 163 replaced by 157 and extended by _R. J. Mathar_, Mar 05 2009

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