OFFSET
1,1
COMMENTS
Exactly one integer exists between each p(n+2) and p(n) which is divisible by (p(n+2)-p(n)).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
Between the primes 19 and 29 is the composite 20 and 20 is divisible by (29-19)=10. So 20 is in the sequence.
MATHEMATICA
For[n = 1, n < 50, n++, s := Prime[n] + 1; While[Floor[s/(Prime[n + 2] -Prime[n])] != s/(Prime[n + 2] - Prime[n]), s++ ]; Print[s]] (* Stefan Steinerberger, Feb 10 2006 *)
idp[n_]:=Module[{p1=Prime[n], p2=Prime[n+2]}, Select[Range[p1+1, p2-1], Divisible[ #, p2-p1]&]]; Table[idp[n], {n, 60}]//Flatten (* Harvey P. Dale, May 30 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Nov 08 2005
EXTENSIONS
More terms from Stefan Steinerberger, Feb 10 2006
More terms from R. J. Mathar, Aug 31 2007
STATUS
approved