A259559 Numbers n such that prime(n)-1 and prime(n+1)-1 have the same number of prime factors, including repeats.

3, 4, 10, 12, 19, 29, 34, 36, 45, 46, 50, 61, 85, 89, 91, 104, 112, 117, 118, 119, 129, 130, 137, 138, 143, 147, 148, 158, 178, 179, 181, 185, 200, 202, 206, 214, 220, 233, 238, 239, 244, 248, 249, 258, 262, 275, 299, 304, 314, 333, 338, 340

Offset: 1

Author

Pratik Koirala, Otis Tweneboah, Nathan Fox, Eugene Fiorini, Jun 30 2015

Keywords

• nonn

Comments

Unlike A105403, this sequence appears to be infinite.

Examples

			The prime factors of prime(10)-1 are 2,2,7 and the prime factors of prime(11)-1 are 2,3,5 and so they have the same number of prime factors, including repeats.
		

Crossrefs

Cf. A105403, A259558.

Programs

Mathematica

Select[Range@ 360, PrimeOmega[Prime[#] - 1] == PrimeOmega[Prime[# + 1] - 1] &] (* Michael De Vlieger, Jul 01 2015 *)
Transpose[SequencePosition[Table[PrimeOmega[Prime[n]-1],{n,400}],{x_,x_}]][[1]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, Nov 29 2015 *)

PARI

lista(nn) = {forprime(p=2, nn, if (bigomega(p-1)==bigomega(nextprime(p+1)-1), print1(primepi(p), ", ")););} \\ Michel Marcus, Jul 01 2015