

A020495


Neither square nor square + prime.


6



10, 34, 58, 85, 91, 130, 214, 226, 370, 526, 706, 730, 771, 1255, 1351, 1414, 1906, 2986, 3676, 9634, 21679
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OFFSET

1,1


COMMENTS

Almost certainly finite; no other terms below 2.5*10^7. Search extended to 3*10^9 by James Van Buskirk without finding any more terms.  John Robertson (Jpr2718(AT)aol.com)
Hardy & Littlewood's Conjecture H is that this sequence is finite and that the number of representations of n as the sum of a prime and a square is asymptotically sqrt(n)/log n * prod_{p > 2} 1  (n / p) / (p  1), where (n / p) is the Legendre symbol.
Hongze Li showed that there are at most O(n^0.982) members of this sequence below n, improving on earlier results of Wang.


LINKS



MATHEMATICA

isA020495[n_] := (r = True; If[ IntegerQ[ Sqrt[n]], r = False, Do[ If[ PrimeQ[n  k^2], r = False; Break[]], {k, 0, Sqrt[n]}]; r]); Select[ Range[30000], isA020495] (* JeanFrançois Alcover, Oct 06 2011, after PARI *)


PROG

(PARI) isA020495(n)=if(issquare(n), return(0)); for(k=0, sqrtint(n), if(isprime(nk^2), return(0))); 1


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



EXTENSIONS



STATUS

approved



