A261515 Primes of the form p(q) + p(r) with q and r both prime, where p(.) is the partition function given by A000041.
5, 17, 59, 71, 103, 157, 353, 787, 4567, 4621, 6857, 63317, 124769, 336773, 14178581, 37187119, 214544387, 214811057, 215602631, 271249247, 273928639, 431274143, 544625929, 851377883, 3913864351, 5964539507, 5964539519, 11097645023, 11097974947, 11102342221, 45063304271, 142799017567, 207890420203, 207913758571
Offset: 1
Keywords
Examples
a(1) = 5 since p(2) + p(3) = 2 + 3 = 5 with 2, 3 and 5 all prime. a(2) = 17 since p(2) + p(7) = 2 + 15 = 17 with 2, 7 and 17 all prime.
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
- Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
- Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.
Programs
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Mathematica
f[n_]:=PartitionsP[Prime[n]] n=0;Do[If[PrimeQ[f[k]+f[m]],n=n+1;Print[n," ",f[k]+f[m]]],{m,1,40},{k,1,m}]
Comments