cp's OEIS Frontend

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

%I A101597 #13 Dec 17 2017 03:07:30
%S A101597 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,
%T A101597 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,
%U A101597 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
%N A101597 Number of consecutive composite numbers between balanced primes and their lower or upper prime neighbor.
%C A101597 These numbers are not always prime with 35 occurring for prime(n) n<1000000.
%C A101597 The first 35 occurs at a(947). - _Antti Karttunen_, Dec 16 2017
%H A101597 Antti Karttunen, <a href="/A101597/b101597.txt">Table of n, a(n) for n = 1..10000</a>
%F A101597 a(n) = A013632(A006562(n))-1. - _Antti Karttunen_, Dec 16 2017
%e A101597 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.
%t A101597 Flatten[Differences /@ Select[Partition[Prime@ Range[1900], 3, 1], #2 == Mean@ {#1, #3} & @@ # &][[All, 1 ;; 2]] - 1] (* _Michael De Vlieger_, Dec 16 2017 *)
%o A101597 (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",")) ) }
%o A101597 (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
%Y A101597 Cf. A006562, A013632.
%K A101597 nonn
%O A101597 1,2
%A A101597 _Cino Hilliard_, Jan 26 2005
%E A101597 Offset changed from 2 to 1 by _Antti Karttunen_, Dec 16 2017