A125191 Primes of the form k# + (k+1)# +- 1, where k# = A002110(k) = primorial(k).
2, 7, 37, 239, 241, 2521, 32341, 540539, 540541, 232792559, 232792561, 207030183359, 311671001662019, 41287621429375723111588738861, 5801527386969669153864265802424086050777441586253956297278498679
Offset: 1
Keywords
Examples
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.
Programs
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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
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Mathematica
plim=45;k= FoldList[Times, 1, Prime[Range[plim]]];m=Table[k[[l]]+k[[l+1]],{l,plim}];Sort[Select[Join[m+1,m-1],PrimeQ]] (* James C. McMahon, Dec 15 2024 *) Join[{2},Select[Sort[Flatten[#+{1,-1}&/@(Total/@Partition[FoldList[Times,Prime[Range[40]]],2,1])]],PrimeQ]] (* Harvey P. Dale, Jul 15 2025 *) -
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)
Extensions
Edited, corrected and extended by Klaus Brockhaus and R. J. Mathar, Jan 25 2007
Comments