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A047847
Numbers n such that n + (n+1) and (n+2) + (n+3) are both prime.
2
1, 3, 6, 9, 18, 21, 33, 39, 48, 51, 54, 63, 81, 96, 111, 114, 138, 153, 156, 174, 189, 198, 219, 228, 231, 243, 249, 306, 321, 336, 369, 378, 384, 411, 426, 429, 438, 441, 453, 468, 483, 504, 543, 546, 606, 639, 648, 651, 711, 714, 723, 741, 744, 774, 783, 789
OFFSET
1,2
COMMENTS
Except for the first one, all terms are multiples of 3, as can be seen from the formula a(n+1) = 3*A056956(n). - Zak Seidov, Aug 26 2012
LINKS
FORMULA
a(n) = (A023200(n)-1)/2 = (A046132(n)-5)/2 = 3*A056956(n-1) (for n>1).
EXAMPLE
If n = 6, then 6 + 7 = 13 and 8 + 9 = 17 are both prime.
MATHEMATICA
Select[Range[790], And @@ PrimeQ[{2*# + 1, 2*# + 5}] &] (* Jayanta Basu, Aug 11 2013 *)
Select[Range[800], AllTrue[2#+{1, 5}, PrimeQ]&] (* Harvey P. Dale, Jan 28 2023 *)
PROG
(PARI) is_A047847(n)=isprime(n*2+1)&isprime(n*2+5) \\ - M. F. Hasler, Aug 26 2012
CROSSREFS
Sequence in context: A127644 A324283 A161338 * A007783 A363128 A050625
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Corrected by Henry Bottomley, Jul 18 2000
STATUS
approved