OFFSET
1,1
COMMENTS
A number n is in this sequence iff n and n+1 is in A175590; also: iff n and n+2 are in A052214 (in which case n+1 is in A052214, too); and also: iff {n,n+1,n+2,n+3} are in A052213.
a(62) = a(63)-1 = 380480345 = A034173(6) is the first term n such that n+1 is also in the sequence.
Sequence A218455 consists of all such terms a(n) = a(n+1)-1, and A218865 lists those for which a(n) = a(n+2)-2. - M. F. Hasler, Apr 27 2026
From David A. Corneth, Apr 28 2026: (Start)
Each of a(n), a(n)+1, a(n)+2, a(n)+3, a(n)+4 may not be squarefree. Proof: Of five consecutive numbers at least one of them must be divisible by 4 hence cannot be squarefree. As the others have the same prime signature they also cannot be squarefree.
There is no term divisible by 4 among the first 3000 terms. Is there a term divisible by 4? (End)
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10294 (first 140 terms from M. F. Hasler, terms from n = 141 to 1000 from Donovan Johnson)
PROG
(PARI) is_A218448(n)={my(f); !for(i=0, 4, f!=(f=vecsort(factor(n+i)[, 2]))&& i && return)}
(PARI) f(k)=vecsort(factor(k)[, 2]~, , 4)
t=f(n=2); while(n<1e8, for(i=n+1, n+4, tt=f(i); if(tt!=t, n=i; t=tt; next(2))); print1(n", "); n++) \\ Charles R Greathouse IV, Oct 28 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Oct 28 2012
EXTENSIONS
a(6)-a(8) from Charles R Greathouse IV, Oct 28 2012
a(9)-a(25) from Donovan Johnson, Oct 28 2012
Values up to a(140) computed using b175590.txt from Charles R Greathouse IV - M. F. Hasler, Oct 28 2012
STATUS
approved