A262731 Primes p in the form pi(q^2)+pi(r^2) with q and r both prime, where pi(x) denotes the number of primes not exceeding x.
11, 13, 17, 19, 41, 43, 101, 103, 223, 293, 313, 331, 359, 401, 409, 439, 491, 521, 523, 571, 613, 677, 709, 821, 883, 947, 1009, 1039, 1061, 1193, 1283, 1291, 1303, 1373, 1409, 1427, 1453, 1471, 1487, 1543, 1553, 1609, 1669, 1697, 1811, 1861, 1879, 1907, 1949, 1999, 2039, 2063, 2143, 2213, 2239, 2251, 2267, 2287, 2309, 2381
Offset: 1
Keywords
Examples
a(1) = 11 since 11 = 2 + 9 = pi(2^2) + pi(5^2) with 11, 2 and 5 all prime. a(60) = 2381 since 2381 = 1000 + 1381 = pi(89^2) + pi(107^2) with 2381, 89 and 107 all prime.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..3000 from Zhi-Wei Sun)
Programs
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Mathematica
f[n_]:=PrimePi[Prime[n]^2] T[1]:={f[1]} T[n_]:=Union[T[n-1],{f[n]}] n=0;Do[Do[If[f[x]>Prime[y],Goto[aa]];If[MemberQ[T[y],Prime[y]-f[x]],n=n+1;Print[n," ",Prime[y]];Goto[aa]];Continue,{x,1,y}]; Label[aa];Continue,{y,1,353}]
Comments