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A259540
Least positive integer k such that k and k*n are terms of A259539.
8
60, 326940, 728700, 115020, 375258, 70920, 33150, 297990, 2340, 72870, 858, 1416210, 284130, 78978, 91368, 9438, 5547000, 767760, 1182918, 30468, 485208, 60, 7908810, 916188, 21522, 823968, 87720, 390210, 3252, 72870, 7878, 1823010, 1179990, 98010, 3462, 7878, 280590, 6870, 60, 434460
OFFSET
1,1
COMMENTS
Conjecture: Any positive rational number r can be written as m/n with m and n terms of A259539.
For example, 4/5 = 11673840/14592300 with 11673840 and 14592300 terms of A259539.
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.
EXAMPLE
a(22) = 60 since 60 and 60*22 = 1320 are terms of A259539. In fact, 60-1 = 59, 60+1 = 61, prime(60)+2 = 283, 1320-1 = 1319, 1320+1 = 1321 and prime(1320)+2 = 10861 are all prime.
MATHEMATICA
PQ[k_]:=PrimeQ[Prime[k]+2]&&PrimeQ[Prime[Prime[k]+1]+2]
QQ[n_]:=PrimeQ[n-1]&&PrimeQ[n+1]&&PrimeQ[Prime[n]+2]
Do[k=0; Label[bb]; k=k+1; If[PQ[k]&&QQ[n*(Prime[k]+1)], Goto[aa], Goto[bb]]; Label[aa]; Print[n, " ", Prime[k]+1]; Continue, {n, 1, 40}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jun 30 2015
STATUS
approved