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A259559 Numbers n such that prime(n)-1 and prime(n+1)-1 have the same number of prime factors, including repeats. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A287448 A325235 A135116 * A050187 A101506 A092434

Adjacent sequences:  A259556 A259557 A259558 * A259560 A259561 A259562

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 20 20:04 EDT 2019. Contains 328270 sequences. (Running on oeis4.)