OFFSET
1,1
COMMENTS
The associated prime factors will always include 2 and 3.
Will every prime number be encountered as a prime factor from the sequence entries?
The sequence appears to share many of it terms with A001122.
What is the asymptotic behavior?
Conjecture: sequence has density A271780/2 = A005597*4/Pi^2 = 0.2675535... in the primes. - Charles R Greathouse IV, Jan 24 2018
The prime terms of A179017 (except 3). - Bill McEachen, Oct 21 2021
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Bill McEachen, A269844_vs_A001122
EXAMPLE
277 = 138 + 139 = 2*3*23 + 139 is in the sequence since both terms are squarefree.
281 = 140 + 141 = 2^2*5*7 + 3*47 is not in the sequence since the former term is divisible by 2^2.
MATHEMATICA
Select[Prime@ Range[3, 200], PrimeOmega@ # == PrimeNu@ # &[# (# + 1)] &@ Floor[#/2] &] (* Michael De Vlieger, Mar 07 2016 *)
PROG
(PARI)
genit(maxx)={for(i5=3, maxx, n=prime(i5); a=factor(floor(n/2.)); b=factor(ceil(n/2.)); clear=1; for(j5=1, omega(floor(n/2.)), if(a[j5, 2]<>1, clear=0));
for(j7=1, omega(ceil(n/2.)), if(b[j7, 2]<>1, clear=0)); if(clear>0, print1(n, ", "))); }
(PARI) is(n)=isprime(n) && issquarefree(n\2) && issquarefree(n\2+1) \\ Charles R Greathouse IV, Jan 24 2018
(PARI) list(lim)=my(v=List(), t=1); forfactored(k=3, (lim+1)\2, if(vecmax(k[2][, 2])>1, t=0, ; if(t && isprime(t=2*k[1]-1), listput(v, t)); t=1)); Vec(v) \\ Charles R Greathouse IV, Jan 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bill McEachen, Mar 06 2016
STATUS
approved