A101597 Number of consecutive composite numbers between balanced primes and their lower or upper prime neighbor.

1, 5, 5, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 11, 5, 5, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 11, 5, 5, 5, 5, 5, 11, 5, 5, 5, 5, 11, 11, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Author

Cino Hilliard, Jan 26 2005

Keywords

• nonn

Comments

These numbers are not always prime with 35 occurring for prime(n) n<1000000.

The first 35 occurs at a(947). - Antti Karttunen, Dec 16 2017

Examples

			53 has the 5 consecutive composites 48,49,50,51,52 below it and the 5 consecutive composites 54,55,56,57,58 above it so 5 is in the second position in the table.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006562, A013632.

Programs

Mathematica

Flatten[Differences /@ Select[Partition[Prime@ Range[1900], 3, 1], #2 == Mean@ {#1, #3} & @@ # &][[All, 1 ;; 2]] - 1] (* Michael De Vlieger, Dec 16 2017 *)

PARI

betwixtpr(n) = { local(c1,c2,x,y); for(x=2,n, c1=c2=0; for(y=prime(x-1)+1,prime(x)-1, if(!isprime(y),c1++); ); for(y=prime(x)+1,prime(x+1)-1, if(!isprime(y),c2++); ); if(c1==c2,print1(c1",")) ) }

PARI

up_to = 10000; n = 0; forprime(p=1, oo, if((d=(p-precprime(p-1)))==(nextprime(p+1)-p), n++; write("b101597.txt", n, " ", d-1); if(n>=up_to,break))); \\ Antti Karttunen, Dec 16 2017

Formula

a(n) = A013632(A006562(n))-1. - Antti Karttunen, Dec 16 2017

Extensions

Offset changed from 2 to 1 by Antti Karttunen, Dec 16 2017