OFFSET
1,1
COMMENTS
The sequence contains some terms such that m and m + 2k (k > 1) have the same prime signature. For some terms where m and m + 2k share the same prime signature this means that every alternate element between, and including m and m + 2k have the same prime signature. The first such example is where a(41951) = 402677, a(41953) = 402679, and a(41955) = 402681, share the same prime signature {1, 1}. Also the remaining alternate terms excluding endpoints share the same prime signature. Using the above example, a(41952) = 402678 and a(41954) = 402680 share the prime signature {1,1,3}. - Torlach Rush, Feb 25 2018
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5585 from Michel Marcus)
EXAMPLE
18 is a term because 18 = 2 * 3^2 and 18 + 2 = 20 = 2^2 * 5.
19 is not a term because it is prime and 21 is the product of two primes, so the prime signatures are different.
MATHEMATICA
primeSignature[n_] := Sort[Transpose[FactorInteger[n]][[2]]]; Select[ Range[2, 1000], primeSignature[#] == primeSignature[# + 2] &] (* Adapted from A052213 *)
PROG
(PARI) isok(n) = vecsort(factor(n)[, 2]) == vecsort(factor(n+2)[, 2]); \\ Michel Marcus, Feb 25 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Dec 18 2016
STATUS
approved