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%I #16 Nov 14 2022 23:05:06
%S 0,75,1380,1725,4575,7095,10020,10620,31800,38355,58710,61170,67125,
%T 92235,92310,94845,118530,137415,156000,168765,189705,238815,249450,
%U 257370,339375,353925,507270,584265,590040,617265,625845,631740,761760,845295,866910,943605
%N Numbers k for which 2*k+7, 4*k+7, 6*k+7, 8*k+7, 10*k+7 and 12*k+7 are primes.
%C Conjecture. For every odd prime p there exist infinitely many numbers k for which 2*k+p, 4*k+p, ..., 2*(p-1)*k+p are primes.
%C For p=3, cf. A115334, for p=5, cf. A210504. This sequence corresponds to p=7.
%C In general case of prime p, every k == 0 (mod Product{p_2*p_3*...*p_k)), where p_k is the maximal prime < p.
%F a(n) == 0 (mod 15).
%t Select[Range[0, 1000000], PrimeQ[2*# + 7] && PrimeQ[4*# + 7] && PrimeQ[6*# + 7] && PrimeQ[ 8*# + 7] && PrimeQ[ 10*# + 7] && PrimeQ[ 12*# + 7] &] (* _T. D. Noe_, Jan 25 2013 *)
%Y Cf. A115334, A210504.
%K nonn
%O 0,2
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Jan 25 2013
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