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a(n) is the largest m such that A182134(n - k) = k for A246785(n) <= k <= m, or zero if there is no such m.
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%I #17 Dec 09 2014 10:57:06

%S 1,1,1,1,0,2,2,2,0,2,2,2,0,3,3,2,0,3,0,4,0,4,3,2,0,0,4,0,5,2,2,0,3,0,

%T 4,4,0,4,4,4,4,0,4,0,5,4,2,0,0,4,0,5,5,4,4,0,0,5,0,6,5,3,0,0,4,4,4,0,

%U 0,0,5,5,5,5,5,5,5,5,5,4,4,4,0,5,0,6,0,0,7

%N a(n) is the largest m such that A182134(n - k) = k for A246785(n) <= k <= m, or zero if there is no such m.

%C Recall that A182134(k) is the number of primes p with prime(k) < p < prime(k)^(1+1/k). Obviously a(n) = 0 if and only if A246785(n) = 0.

%H Robert Price, <a href="/A246793/b246793.txt">Table of n, a(n) for n = 1..10000</a>

%e A182134(217 - k) = k for k = 3, 4, ..., 9 since A246785(217) = 3 and a(217) = 9.

%t np[n_]:= If[n==0, 0, (i=Prime[n]+1; j=Prime[n]^(1+1/n); Length[Select[Range[i,j], PrimeQ]])]; a1[n_]:= (For[m=1, m<=n-1&& np[n-m] != m, m++];m);a2[k_]:= If[c=a1[k]; c==k,0,c]; a[n_]:= If[a2[n]==0, 0, For[r=a2[n], np[n-r]==r, r++]; r-1]; Table[a[k], {k,2,90}]

%Y Cf. A000040, A182134, A246785, A246790.

%K nonn

%O 1,6

%A _Farideh Firoozbakht_, Oct 24 2014