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%I #4 Mar 30 2012 17:22:34
%S 1,21,45,51,81,213,249,315,477,525,681,891,1143,1221,1851,1965,2415,
%T 5133
%N Numbers n such that there are no primes < 2n in the sequence m(0)=n, m(k+1)=m(k)+4k.
%C No others < 10^8. Note that 3 divides all these n > 1. This sequence is conjectured to be complete. Related to a question posed in A036468 by Zhang Ming-Zhi. Let r=2s+1 be an odd number. If n = (s+1)^2+s^2, then the sequence m(0)=n, m(k+1)=m(k)+4k for k=0,1,...s calculates the s+1 distinct sums of two squares (r-i)^2+i^2.
%e 45 is here because 45, 49, 57, 69 and 85 are all composite.
%t lst={}; Do[n=m; found=False; k=0; While[n=n+4k; !found && n<2m, found=PrimeQ[n]; k++ ]; If[ !found, AppendTo[lst, m]], {m, 1, 10000, 2}]; lst
%Y Cf. A036468 (number of ways to represent 2n+1 as a+b with a^2+b^2 prime).
%K nonn
%O 1,2
%A _T. D. Noe_, Oct 17 2004
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