

A101597


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

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


LINKS



FORMULA



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(x1)+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=(pprecprime(p1)))==(nextprime(p+1)p), n++; write("b101597.txt", n, " ", d1); if(n>=up_to, break))); \\ Antti Karttunen, Dec 16 2017


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



