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A210505 Numbers n for which 2*n+7, 4*n+7, 6*n+7, 8*n+7, 10*n+7 and 12*n+7 are primes. 0
0, 75, 1380, 1725, 4575, 7095, 10020, 10620, 31800, 38355, 58710, 61170, 67125, 92235, 92310, 94845, 118530, 137415, 156000, 168765, 189705, 238815, 249450, 257370, 339375, 353925, 507270, 584265, 590040, 617265, 625845, 631740, 761760, 845295, 866910, 943605 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Conjecture. For every odd prime p there exists infinite sequence of n for which 2*n+p, 4*n+p, ..., 2*(p-1)*n+p are primes.

For p=3, cf. A115334, for p=5, cf. A210504. This sequence corresponds to p=7.

In general case of prime p, every n==0 (mod prod{p_2*p_3*...*p_k)), where p_k is the maximal prime<p.

LINKS

Table of n, a(n) for n=0..35.

FORMULA

a(n)==0 (mod15)

MATHEMATICA

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 *)

CROSSREFS

Cf. A115334, A210504.

Sequence in context: A285920 A293581 A210047 * A285856 A202257 A278154

Adjacent sequences:  A210502 A210503 A210504 * A210506 A210507 A210508

KEYWORD

nonn

AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Jan 25 2013

STATUS

approved

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Last modified October 16 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)