OFFSET
1,2
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 have already the prime sum we need.
a(3) = 7 as a(3) = 3, 4, 5 or 6 would produce at least a prime sum too many.
a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce at least a prime sum too many.
a(5) = 13 as a(5) = 3, 4, 5, 6, 9, 10, 11 or 12 would also produce at least one prime sum too many.
a(6) = 14 as a(6) = 14 doesn't produce an extra prime sum - only composite sums.
a(7) = 19 as a(7) = 15, 16, 17 or 18 would produce at least a prime sum too many.
a(8) = 36 is the smallest available integer that produces the single prime sum we need among the last 7 integers {2, 7, 8, 13, 14, 19, 36}, which is 43 = 36 + 7.
And so on.
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Nov 13 2019
STATUS
approved