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A126655 Numbers n such that 6*p(n)-1 and 6*p(n)+1 are twin primes and 6*p(n+1)-1 and 6*p(n+1)+1 are also twin primes with p(n) = n-th prime. 1

%I #11 Oct 10 2019 13:42:14

%S 1,2,3,27,137,340,479,882,1415,1883,3442,3798,4284,5827,7559,8783,

%T 9453,10355,10731,11388,12565,13613,16477,17007,18402,18665,19450,

%U 19633,22306,24971,25083,29108,29861,30748,31694,32622,33097,36743,37141

%N Numbers n such that 6*p(n)-1 and 6*p(n)+1 are twin primes and 6*p(n+1)-1 and 6*p(n+1)+1 are also twin primes with p(n) = n-th prime.

%H Harvey P. Dale, <a href="/A126655/b126655.txt">Table of n, a(n) for n = 1..1000</a>

%e 6*2-1=11 6*2+1=13 11 13 twin primes as 17 and 19 so 1 is first term of the sequence

%e 6*3-1=17 6*3+1=19 17 19 twin primes as 29 and 31 so 2 is second term of the sequence

%e 6*5-1=29 6*5+1=31 29 and 31 twin primes 5=3rd prime

%e 6*7-1=41 6*7+1=43 41 and 43 twin primes 7=4th prime so 3 is the 3rd term of the sequence

%t Select[Range[39000], PrimeQ[6*Prime[ # ] - 1] && PrimeQ[6*Prime[ # ] + 1] && PrimeQ[6*Prime[ # + 1] - 1] && PrimeQ[6*Prime[ # + 1] + 1] &] (* _Ray Chandler_, Feb 11 2007 *)

%t Select[Range[40000],AllTrue[Flatten[{6*Prime[#]+{1,-1},6*Prime[#+1]+{1,-1}}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Nov 27 2015 *)

%Y Cf. A060212.

%K nonn

%O 1,2

%A _Pierre CAMI_, Feb 09 2007

%E Corrected and extended by _Ray Chandler_, Feb 11 2007

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Last modified June 20 18:00 EDT 2024. Contains 373532 sequences. (Running on oeis4.)