A113729 - OEIS

%I #13 May 07 2015 18:15:54

%S 5,8,8,10,16,20,24,24,28,36,36,40,48,48,56,56,60,72,72,72,80,90,90,98,

%T 100,104,110,120,110,120,132,144,140,144,154,160,160,176,168,180,182,

%U 192,192,198,208,224,216,230,228,240,234,252,242,252,266,266,276,276

%N a(n) is the integer between p(n) and p(n+3) which is divisible by (p(n+3)-p(n)), where p(n) is the n-th prime.

%C Exactly one integer exists between each p(n+3) and p(n) which is divisible by (p(n+3)-p(n)).

%H Harvey P. Dale, <a href="/A113729/b113729.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n)=p(n+3) - (p(n) (mod p(n+3)-p(n))).

%e Between the primes 19 and 31 is the composite 24 and 24 is divisible by (31-19)=12. So 24 is in the sequence.

%t f[n_] := Block[{p = Prime[n], q = Prime[n + 3]}, q - Mod[p, q - p]]; Table[ f[n], {n, 58}] (* _Robert G. Wilson v_ *)

%t id[{a_,b_,c_,d_}]:=Select[Range[a+1,d-1],Divisible[#,d-a]&]; Flatten[ id/@ Partition[Prime[Range[70]],4,1]] (* _Harvey P. Dale_, May 07 2015 *)

%Y Cf. A113709, A113728.

%K nonn

%O 1,1

%A _Leroy Quet_, Nov 08 2005

%E More terms from _Robert G. Wilson v_, Nov 09 2005