OFFSET
1,1
COMMENTS
REFERENCES
Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..500 from Zhi-Wei Sun)
Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.
EXAMPLE
a(1) = 13 since pi(13^2) = pi(169) = 39 = 9 + 30 = pi(5^2) + pi(11^2) with 13, 5 and 11 distinct primes.
MATHEMATICA
f[n_]:=PrimePi[Prime[n]^2]
T[n_]:=Table[f[k], {k, 1, n}]
n=0; Do[Do[If[2*f[k]>=f[m], Goto[aa]]; If[MemberQ[T[m-1], f[m]-f[k]], n=n+1; Print[n, " ", Prime[m]]; Goto[aa]]; Continue, {k, 1, m-1}]; Label[aa]; Continue, {m, 1, 541}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Sep 23 2015
STATUS
approved