A163757 The count of primes between the n-th unsafe and the n-th safe prime.

1, 1, 0, 1, 6, 6, 11, 15, 25, 26, 32, 37, 49, 51, 54, 68, 67, 70, 76, 79, 98, 115, 118, 121, 132, 136, 159, 171, 176, 176, 178, 185, 192, 196, 210, 234, 244, 258, 258, 259, 264, 275, 308, 308, 318, 351, 357, 359, 365, 367, 370, 379, 382, 386, 418, 438, 455, 457, 462, 473, 477

Offset

1,5

Comments

For n=3, where the 3rd unsafe prime is larger than the 3rd safe prime, there are two primes in between which could formally be counted as -2, but have been replaced by 0 here.

Links

Table of n, a(n) for n=1..61.

Formula

a(n) = max( 0, A000720(A005385(n)-1)-A000720(A059456(n)) ).

Example

a(1)=1 counts one prime (the 3) between 2 and 5;
a(2)=1 counts one prime (the 5) between 3 and 7;
a(5)=6 counts the primes from 23 to 43 between 19 and 53.

Maple

isA005385 := proc(n) if isprime(n) then isprime( (n-1)/2 ) ; else false; fi; end:
isA059456 := proc(n) if isprime(n) then not isprime( (n-1)/2 ) ; else false; fi; end:
A059456 := proc(n) if n = 1 then 2; else for a from procname(n-1)+1 do if isA059456(a) then RETURN(a) ; fi; od: fi; end:
A005385 := proc(n) if n = 1 then 5; else for a from procname(n-1)+1 do if isA005385(a) then RETURN(a) ; fi; od: fi; end:
A000720 := proc(n) numtheory[pi](n) ; end:
A163757 := proc(n) max(0, A000720(A005385(n)-1)-A000720(A059456(n))) ; end: seq(A163757(n), n=1..80) ; # R. J. Mathar, Aug 06 2009

Crossrefs

Cf. A000040, A005385, A059456.

Sequence in context: A046605 A095899 A346530 * A109538 A212534 A173319

Adjacent sequences: A163754 A163755 A163756 * A163758 A163759 A163760

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 03 2009

Extensions

Corrected by R. J. Mathar, Aug 06 2009

Status

approved