A246792 Smallest number m such that for 0 < k < n+1, np(m+k-1) = np(m)-k+1, where np(t) is number of primes p with prime(t) < p < prime(t)^(1 + 1/t).

1, 7, 25, 25, 181, 208, 208, 1867, 14345, 19609, 40918, 40918, 620326, 2552265, 2552265, 7225612, 7225612, 16679492, 33772734, 33772734, 33772734, 620326386, 1516416904, 1516416904, 4764006481, 5272314878, 21423652192

Offset: 1

Author

Farideh Firoozbakht, Oct 16 2014

Keywords

• nonn

Comments

np(m) = A182134(m).

According to the definition, numbers np(a(n)), np(a(n)+1), ..., np(a(n)+n-2) and np(a(n)+n-1) are n consecutive numbers in descending order.

a(34) > 10^12. - Robert Price, Dec 07 2014

See A251736 for the corresponding values of np.

Examples

			a(15) = 2552265, since np(2552265) = 24, np(2552265+1) = 23 , ..., np(2552265+13) = 11, np(2552265+14) = 10 are 15 consecutive numbers in descending order.
		

Links

• Robert Price, Table of n, a(n) for n = 1..33

Crossrefs

Cf. A000040, A182134, A246791, A251736.

Programs

Mathematica

np[t_] := np[t] = Length[Select[Range[Prime[t]+1,Prime[t]^(1+1/t)],PrimeQ]]; a[1]=1; a[n_] := a[n] = (For[m = a[n-1],c = Table[np[m+k-1],{k,n}]; c !=  Reverse[Range[Min[c], Max[c]]], m++]; m); Do[Print[a[n]],{n,15}]

PARI

np(n) = primepi(prime(n)^(1+1/n))-n;
isok(m, n) = {for (k=1, n, if (np(m+k-1) != np(m)-k+1, return (0));); return (1);}
a(n) = {m = 1; while (! isok(m, n), m++); m;} \\ Michel Marcus, Dec 07 2014

Extensions

a(18)-a(33) from Robert Price, Dec 07 2014