A131101 Numbers that when added it to their prime factors +1 the result is a prime number, member of A131102.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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: A073880 A118332 A118333 * A188534 A214196 A246857

Adjacent sequences: A131098 A131099 A131100 * A131102 A131103 A131104

Keyword

easy,nonn

Author

Tomas Xordan, Jun 14 2007

Status

approved