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.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..50.

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

Sequence in context: A283159 A283145 A191145 * A214345 A166109 A157755

Adjacent sequences: A145351 A145352 A145353 * A145355 A145356 A145357

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