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.

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

Author

Farideh Firoozbakht, Oct 24 2014

Keywords

• nonn

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.

Examples

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

Links

• Robert Price, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A182134, A246785, A246790.

Programs

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}]