OFFSET
1,1
COMMENTS
Subsequence of A005843, same as A113935 with first term (5) excluded, since it is odd, not even. Index in A056240 of terms in A288313 (except for first two terms 2,4 of latter).
The terms in this sequence, combined with those in A297925 and A298366 form a partition of A005843(n); n>=3 (nonnegative numbers>=6). This is because any even integer n>=6 satisfies either(i) n-3 is prime, (ii) n-5 prime but n-3 composite, or (iii) n-5 and n-3 both composite.
a(n) is the smallest even number e > prime(n+1) such that e has a Goldbach partition containing prime(n+1). - Felix Fröhlich, Aug 18 2019
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..5000
FORMULA
a(n) = A113935(n+1), n>=1.
a(n) = prime(n + 1) + 3 = A113935(n + 1). - David A. Corneth, Mar 23 2018
EXAMPLE
MAPLE
N:=200
for n from 6 to N by 2 do
if isprime(n-3) then print(n);
end if
end do
MATHEMATICA
Select[2 Range@125, PrimeQ[# - 3] &] (* Robert G. Wilson v, Jan 15 2018 *)
Select[Prime[Range[100]]+3, EvenQ] (* Harvey P. Dale, Mar 07 2022 *)
PROG
(PARI) a(n) = prime(n + 1) + 3 \\ David A. Corneth, Mar 23 2018
(GAP) Filtered([1..300], n->IsEvenInt(n) and IsPrime(n-3)); # Muniru A Asiru, Mar 23 2018
(Magma) [NthPrime(n+1) +3: n in [1..70]]; // G. C. Greubel, May 21 2019
(Sage) [nth_prime(n+1) +3 for n in (1..70)] # G. C. Greubel, May 21 2019
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
David James Sycamore, Jan 15 2018
STATUS
approved