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Smallest integer >= 2 that is not the sum of 2 positive integers whose prime factors are all <= p(n), the n-th prime.
4

%I #18 Sep 21 2017 09:03:16

%S 3,7,23,71,311,479,1559,5711,10559,18191,31391,118271,366791,366791,

%T 2155919,2155919,2155919,6077111,6077111,98538359,120293879,131486759,

%U 131486759,508095719,2570169839,2570169839,2570169839,2570169839,2570169839,2570169839

%N Smallest integer >= 2 that is not the sum of 2 positive integers whose prime factors are all <= p(n), the n-th prime.

%C Here we are taking 1 to be the zeroth prime.

%C a(30) > 2570169839. - _Donovan Johnson_, Aug 31 2010

%D Computed by _David W. Wilson_, Jun 29 2001.

%e a(1): 2=1+1, 3=1+2, 4=2+2, 5=1+4, 6=2+4, but 7 cannot be written as the sum of two positive integers whose prime factors are all <= 2, so a(1) = 7. a(2): 7=3+4, 8=4+4, 9=1+8, ..., 22=4+18, but 23 cannot be so written, so a(2) = 23.

%Y So far it agrees with A045535. Is this a coincidence or a theorem?

%K nonn,nice

%O 0,1

%A Richard C. Schroeppel, Jun 27 2001

%E More terms from _Jud McCranie_, Nov 01 2001

%E a(23)-a(29) from _Donovan Johnson_, Aug 31 2010