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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
OFFSET
1,1
COMMENTS
Unlike A105403, this sequence appears to be infinite.
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
Sequence in context: A325235 A135116 A362743 * A050187 A101506 A362553
KEYWORD
nonn
STATUS
approved