A164266 The count of primes between the n-th and (n+1)-st perfect number.

6, 85, 928, 2062427, 391549471, 5192879231, 55890478433197117

Offset

1,1

Links

Table of n, a(n) for n=1..7.

Formula

a(n) = A000720(A000396(n+1)) - A000720(A000396(n)).

Example

a(1) = 6 counts the 6 primes 7, 11, 13, 17, 19 and 23 between 6 and 28.
a(2) = 85 counts the 85 primes 29, 31, ..., 487, 491 between 28 and 496.

Mathematica

PrimePi[Last[#]]-PrimePi[First[#]]&/@(Partition[(# (#+1))/2&/@ Select[ 2^Range[30]-1, PrimeQ], 2, 1]) (* Harvey P. Dale, Dec 27 2011 *)

Crossrefs

First differences of A185174.

Cf. A000040, A000396, A000720.

Sequence in context: A284522 A167252 A290011 * A136597 A381243 A064329

Adjacent sequences: A164263 A164264 A164265 * A164267 A164268 A164269

Keyword

nonn,hard,more

Author

Juri-Stepan Gerasimov, Aug 11 2009

Extensions

Edited by R. J. Mathar, Aug 26 2009

More terms from Harvey P. Dale, Dec 27 2011

a(7) from the data at A185174 added by Amiram Eldar, Sep 03 2024

Status

approved