login
A131101
Numbers that when added it to their prime factors +1 the result is a prime number, member of A131102.
2
1, 2, 3, 5, 11, 23, 27, 29, 30, 32, 36, 41, 53, 60, 66, 75, 78, 83, 89, 113, 114, 117, 130, 131, 132, 138, 140, 171, 173, 175, 179, 186, 191, 204, 220, 233, 239, 240, 246, 251, 255, 258, 260, 276, 279, 281, 285, 286, 293, 308, 310, 325, 338, 340, 354, 359, 363
OFFSET
1,2
COMMENTS
The Sophie Germain prime numbers (A005384) are part of this sequence because when adding to one of them its only prime factor (itself) + 1 = 2*A005384 + 1 the result is another prime number (A005385)
Prime factors taken with multiplicity. - Harvey P. Dale, Sep 04 2024
LINKS
FORMULA
a(n)+ prime factors of a(n) + 1 = p ; p is a prime number, member of A131102.
EXAMPLE
a(8)=29 because 29 + its only prime factor (itself) + 1 = 29+29+1= 59, and 59 is a prime number = A131102(8) = A005385(6).
a(9)=30 because 30 + its prime factors + 1 = 30 +(2+3+5)+1 =41, and 41 is a prime number = A131102(9).
MATHEMATICA
Select[Range[400], PrimeQ[Total[Times@@@FactorInteger[#]]+#+1]&] (* Harvey P. Dale, Sep 04 2024 *)
CROSSREFS
Sequence in context: A376856 A118332 A118333 * A188534 A214196 A246857
KEYWORD
easy,nonn
AUTHOR
Tomas Xordan, Jun 14 2007
STATUS
approved