OFFSET
1,2
COMMENTS
For all n >= 1, there is exactly one prime in {a(n+i) + a(n+j), 0 <= i < j <= 3}. See A329450, A329452 onwards for variants for nonnegative integers. - M. F. Hasler, Nov 14 2019
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 1 by minimality.
a(2) = 2 as 2 is the smallest available integer not leading to a contradiction. Note that as 1 + 2 = 3 we already have our prime sum.
a(3) = 7 as a(3) = 3, 4, 5 or 6 would produce one prime sum too many.
a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce one prime sum too many.
a(5) = 4 as a(5) = 3 would produce two primes instead of one (3 + 2 = 5 and 3 + 8 = 11); with a(5) = 4 we have the single prime sum we need among the last 4 integers {2,7,8,4}: 11 = 4 + 7.
And so on.
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Nov 13 2019
STATUS
approved