A253257 Least positive integer k such that prime(k*n) has the form p^2 - 2 with p prime, or 0 if no such k exists.
1, 2, 3, 1, 3, 12, 47, 9, 1, 100, 502, 6, 3, 1817, 1, 362, 3141, 4, 104, 50, 14157, 251, 222, 3, 27, 76, 25, 5423, 416, 73, 28764, 181, 488, 3860, 1249, 2, 138, 52, 1, 25, 8734, 65719, 7089, 214, 15, 111, 7, 990, 6254, 20, 1047, 38, 367, 880, 435, 3712, 3287, 208, 5194, 598
Offset: 1
Keywords
Examples
a(1) = 1 since prime(1*1) = 2 = 2^2-2 with 2 prime. a(6) = 12 since prime(12*6) = 359 = 19^2-2 with 19 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..800
- Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.
Programs
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Mathematica
SQ[n_]:=IntegerQ[Sqrt[n]]&&PrimeQ[Sqrt[n]] Do[k=0;Label[bb];k=k+1;If[SQ[Prime[k*n]+2],Goto[aa],Goto[bb]];Label[aa];Print[n, " ", k];Continue,{n,1,60}] -
Perl
use ntheory ":all"; use Math::Prime::Util::PrimeArray qw/$probj/; my %v; forprimes { undef $v{$*$-2} } 4e7; for my $n (1..800) { my $k=1; $k++ until exists $v{$probj->FETCH($k*$n-1)}; say "$n $k"; } # Dana Jacobsen, Dec 15 2015
Comments