A261513 Least positive integer k with p(prime(k))+p(prime(k*n)) prime, where p(.) is the partition function given by A000041.
1, 46, 1, 115, 1, 9, 4, 17, 1, 3, 12, 6, 5, 3, 2, 1253, 1035, 716, 4028, 6154, 9, 3, 1219, 94, 64, 195, 1545, 9909, 365, 52, 182, 76, 277, 135, 1321, 1619, 9693, 5485, 8001, 946, 1, 36, 7154, 10354, 1, 2157, 33, 1344, 1, 39, 1698, 732, 24505, 1, 637, 14, 8, 2127, 1460
Offset: 2
Keywords
Examples
a(2) = 1 since p(prime(1)) + p(prime(1*2)) = p(2) + p(3) = 2 + 3 = 5 is prime. a(3) = 46 since p(prime(46)) + p(prime(46*3)) = p(199) + p(787) = 3646072432125 + 3223934948277725160271634798 = 3223934948277728806344066923 is 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 = 2..100
- Zhi-Wei Sun, Checking the conjecture for r = a/b with 1 <= a < b <= 37
- 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]] Do[k=0;Label[bb];k=k+1;If[PrimeQ[f[k]+f[k*n]],Goto[aa],Goto[bb]];Label[aa];Print[n," ", k];Continue,{n,2,60}]
Comments