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A098078 Table(n,j) of primes p = k*prime(n)#/210-j, where k is the least integer such that p and p+8 are consecutive primes, for n > 4 and j=7 to 1. 2

%I #18 Feb 13 2013 10:51:37

%S 389,401,479,359,701,449,1979,8573,6143,13151,5573,16871,1571,4289,

%T 72923,12149,432713,444869,209063,221219,495923,2771333,6050753,

%U 3787493,7621181,2586581,3094661,20785049,478056143,103047653,333576953

%N Table(n,j) of primes p = k*prime(n)#/210-j, where k is the least integer such that p and p+8 are consecutive primes, for n > 4 and j=7 to 1.

%C In the definition, "prime(n)#" denotes the primorial A002110(n).

%C This is a table with 7 columns, numbered j=7,6,...,1, in each row.

%C All terms are a(n)==5 (mod 6). - _M. F. Hasler_, Feb 13 2013

%e For n = 5, P(5)#/210 = 11,

%e 36*11 - 7 = 389; 389 and 397 consecutive primes with gap of 8.

%e 37*11 - 6 = 401; 401 and 409 consecutive primes with gap of 8.

%e 44*11 - 5 = 479; 479 and 487 consecutive primes with gap of 8.

%e 33*11 - 4 = 359; 359 and 367 consecutive primes with gap of 8.

%e 64*11 - 3 = 701; 701 and 709 consecutive primes with gap of 8.

%e 41*11 - 2 = 449; 449 and 457 consecutive primes with gap of 8.

%e 180*11 - 1 = 1979; 1979 and 1987 consecutive primes with gap of 8.

%o (PARI) A098078(n,j)=forstep(p=-j,1<<99,prod(i=1,n,prime(i))/210, p%6==5 & nextprime(p+2)-p==8 & isprime(p) & return(p)) \\ - _M. F. Hasler_, Feb 13 2013

%Y Cf. A098079.

%K nonn,less,tabf

%O 5,1

%A _Pierre CAMI_, Sep 13 2004

%E Edited and corrected a(34) and a(35), following an observation by _Charles R Greathouse IV_, by _M. F. Hasler_, Feb 13 2013

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Last modified September 8 03:40 EDT 2024. Contains 375749 sequences. (Running on oeis4.)