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A125191 Primes of the form k# + (k+1)# +- 1, where k# = A002110(k) = primorial(k). 2

%I

%S 2,7,37,239,241,2521,32341,540539,540541,232792559,232792561,

%T 207030183359,311671001662019,41287621429375723111588738861,

%U 5801527386969669153864265802424086050777441586253956297278498679

%N Primes of the form k# + (k+1)# +- 1, where k# = A002110(k) = primorial(k).

%C Prime numbers n such that n = (prime(k+1) + 1)*k# +- 1 for some k.

%e Let k = 1; then 1#+2# = 2+6 = 8, 8-1 = 7 is prime but 8+1 = 9 is nonprime.

%e Let k = 3; then 3#+4# = 30+210 = 240, 240-1 = 239 is prime and 240+1 = 241 is also prime.

%p A002110 := 1 : A000040 := 2 : for n from 1 to 38 do if isprime(A002110*(1+A000040)-1) then printf("%d,",A002110*(1+A000040)-1) ; fi ; if isprime(A002110*(1+A000040)+1) then printf("%d,",A002110*(1+A000040)+1) ; fi ; A002110 := A002110*A000040 : A000040 := nextprime(A000040) : od : # _R. J. Mathar_, Jan 26 2007

%o (PARI) {m=37;for(n=0,m,p=primorial(n)+primorial(n+1);if(isprime(a=p-1),print1(a,","));if(isprime(a=p+1),print1(a,",")))} \\ _Klaus Brockhaus_, Jan 25 2007

%Y Cf. A002110 (primorial numbers), A006862 (Euclid numbers), A057588 (Kummer numbers).

%K nonn

%O 1,1

%A _Tomas Xordan_, Jan 12 2007

%E Edited, corrected and extended by _Klaus Brockhaus_ and _R. J. Mathar_, Jan 25 2007

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)