login
A125191
Primes of the form k# + (k+1)# +- 1, where k# = A002110(k) = primorial(k).
2
2, 7, 37, 239, 241, 2521, 32341, 540539, 540541, 232792559, 232792561, 207030183359, 311671001662019, 41287621429375723111588738861, 5801527386969669153864265802424086050777441586253956297278498679
OFFSET
1,1
COMMENTS
Prime numbers of the form (prime(k+1) + 1)*k# +- 1.
EXAMPLE
Let k = 1; then 1#+2# = 2+6 = 8, 8-1 = 7 is prime (hence a term of the sequence) but 8+1 = 9 is nonprime.
Let k = 3; then 3#+4# = 30+210 = 240, 240-1 = 239 is prime and 240+1 = 241 is also prime, so both are terms.
MAPLE
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
PROG
(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
(PARI) genit(maxx)={arr=List(); for(n=0, maxx, p=factorback(primes(n))+factorback(primes(n+1)); if(ispseudoprime(p-1), listput(arr, p-1)); if(ispseudoprime(p+1), listput(arr, p+1))); arr} \\ Bill McEachen, Jun 21 2021 (from David A. Corneth's code at A002110)
CROSSREFS
Cf. A002110 (primorial numbers), A006862 (Euclid numbers), A057588 (Kummer numbers).
Sequence in context: A245902 A063766 A020040 * A300559 A302859 A338182
KEYWORD
nonn
AUTHOR
Tomas Xordan, Jan 12 2007
EXTENSIONS
Edited, corrected and extended by Klaus Brockhaus and R. J. Mathar, Jan 25 2007
STATUS
approved