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

1,2

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A006562, A013632.

Sequence in context: A135089 A127310 A214925 * A119991 A262947 A265821

Adjacent sequences: A101594 A101595 A101596 * A101598 A101599 A101600

Keyword

nonn

Author

Cino Hilliard, Jan 26 2005

Extensions

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

Status

approved