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A153196 Numbers n such that 6*n+5 and 6*n+7 are twin primes. 2
0, 1, 2, 4, 6, 9, 11, 16, 17, 22, 24, 29, 31, 32, 37, 39, 44, 46, 51, 57, 69, 71, 76, 86, 94, 99, 102, 106, 109, 134, 136, 137, 142, 146, 169, 171, 174, 176, 181, 191, 204, 212, 214, 216, 219, 237, 241, 246, 247, 267, 269, 277, 282, 286, 297, 311, 312, 321, 324, 332 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Appears to be the partial sums of A160273 which are the successive differences (divided by 3) of the average of twin prime pairs divided by 2 (A040040). - Stephen Crowley, May 24 2009

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

FORMULA

a(j) = (A001359(j+1)-5)/6.

a(j) = A002822(j)-1.

EXAMPLE

For n = 0, 6*n+5 = 5 and 6*n+7 = 7 are twin primes;

for n = 99, 6*n+5 = 599 and 6*n+7 = 601 are twin primes.

MAPLE

ZL := []; for p to 1000000 do if `and`(isprime(p), isprime(p+2)) then ZL := [op(ZL), ((p+2)^2-p^2)*(1/8)] end if end do; A160273 := [seq((ZL[i+1]-ZL[i])*(1/3), i = 2 .. nops(ZL)-1)]: ListTools[PartialSums]( A160273 ); # Stephen Crowley, May 24 2009

MATHEMATICA

Select[Range[0, 350], PrimeQ[6 # + 5]&&PrimeQ[6 # + 7]&] (* Vincenzo Librandi, Apr 04 2013 *)

PROG

(MAGMA) [ n: n in [0..335] | IsPrime(6*n+5) and IsPrime(6*n+7) ];

CROSSREFS

Cf. A001359 (lesser of twin primes), A002822 (6n-1, 6n+1 are twin primes).

Cf. A037074. - Vincenzo Librandi, Dec 26 2008

Sequence in context: A303331 A233776 A195526 * A247185 A237685 A220768

Adjacent sequences:  A153193 A153194 A153195 * A153197 A153198 A153199

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Dec 20 2008

EXTENSIONS

Edited and extended by Klaus Brockhaus, Dec 26 2008

STATUS

approved

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)