

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(2m1) = Q, a(2m) = P.


7



5, 7, 17, 23, 37, 43, 67, 73, 101, 113, 149, 157, 197, 211, 257, 277, 331, 347, 401, 421, 487, 509, 577, 601, 677, 709, 787, 821, 907, 937, 1031, 1061, 1163, 1193, 1297, 1361, 1447, 1483, 1601, 1657, 1777, 1811, 1949, 1987, 2129, 2179, 2309, 2357, 2503, 2551
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OFFSET

1,1


COMMENTS

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


LINKS



EXAMPLE

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


CROSSREFS



KEYWORD

nonn


AUTHOR

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


EXTENSIONS

163 replaced by 157 and extended by R. J. Mathar, Mar 05 2009


STATUS

approved



