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A246793
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.
4
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, 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, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 0, 5, 0, 6, 0, 0, 7
OFFSET
1,6
COMMENTS
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.
LINKS
EXAMPLE
A182134(217 - k) = k for k = 3, 4, ..., 9 since A246785(217) = 3 and a(217) = 9.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Oct 24 2014
STATUS
approved