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

1,1

Comments

Unlike A105403, this sequence appears to be infinite.

Links

Table of n, a(n) for n=1..52.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A105403, A259558.

Sequence in context: A325235 A135116 A362743 * A050187 A101506 A362553

Adjacent sequences: A259556 A259557 A259558 * A259560 A259561 A259562

Keyword

nonn

Author

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

Status

approved