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URL: https://oeis.org/A113728

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A113728
a(n) is the integer between p(n) and p(n+2) which is divisible by (p(n+2)-p(n)), where p(n) is the n-th prime.
2
3, 4, 6, 12, 12, 18, 18, 20, 24, 32, 40, 42, 42, 50, 48, 56, 64, 70, 72, 72, 80, 80, 84, 96, 102, 102, 108, 108, 126, 126, 130, 136, 144, 144, 152, 156, 160, 170, 168, 176, 180, 192, 192, 198, 210, 216, 224, 228, 228, 230, 240, 240, 256, 252, 264, 264, 272, 280
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
FORMULA
a(n) = A031131(n)*ceiling(A000040(n)/A031131(n)). - R. J. Mathar, Aug 31 2007
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
Sequence in context: A062822 A175894 A175029 * A000114 A310006 A294144
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