A113709 - OEIS

%I #19 Jan 09 2019 16:07:50

%S 4,6,8,12,16,18,20,24,30,36,40,42,44,48,54,60,66,68,72,78,80,84,96,

%T 100,102,104,108,112,126,128,132,138,140,150,156,162,164,168,174,180,

%U 190,192,196,198,204,216,224,228,232,234,240,250,252,258,264,270,276,280

%N a(n) is the composite between p(n) and p(n+1), where p(n) is the n-th prime, which is divisible by (p(n+1)-p(n)).

%C Exactly one composite exists between each p(n+1) and p(n) which is divisible by (p(n+1)-p(n)), for n >= 2.

%H Harvey P. Dale, <a href="/A113709/b113709.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n)=p(n+1) - (p(n) (mod p(n+1)-p(n))).

%e Between the primes 67 and 71 is the composite 68 and 68 is divisible by (71-67)=4. So 68 is in the sequence.

%t f[n_] := Block[{p = Prime[n], q = Prime[n + 1]}, q - Mod[p, q - p]]; Table[ f[n], {n, 2, 60}] (* _Robert G. Wilson v_ *)

%t cbp[{a_,b_}]:=Select[Range[a+1,b-1],Divisible[#,b-a]&]; cbp/@ Partition[ Prime[ Range[2,100]],2,1]//Flatten (* _Harvey P. Dale_, Jan 09 2019 *)

%Y Cf. A113710, A111379.

%K nonn

%O 2,1

%A _Leroy Quet_, Nov 06 2005

%E More terms from _Don Reble_ and _Robert G. Wilson v_, Nov 07 2005