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A111700
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Number of integers between p(n) and p(n+1) which are coprime to (p(n+1)-p(n)), where p(n) is the n-th prime.
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0
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0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 3, 1, 0, 1, 0, 1, 5, 1, 1, 0, 3, 0, 1, 1, 1, 1, 1, 0, 3, 0, 1, 0, 3, 3, 1, 0, 1, 1, 0, 3, 1, 1, 1, 0, 1, 1, 0, 3, 5, 1, 0, 1, 5, 1, 3, 0, 1, 1, 3, 1, 1, 1, 1, 3, 1, 3, 3, 0, 3, 0, 1, 1, 1, 3, 1, 0, 1, 3, 3, 1, 3, 1, 1, 3, 0, 5, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,24
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FORMULA
| a(n) = phi(p(n+1)-p(n)) - 1, where phi(n) = A000010(n).
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EXAMPLE
| Between the primes p(24) = 89 and p(25) = 97 are 3 integers (91, 93 and 95) which are coprime to (p(25)-p(24)) = 8, so a(24) = 3.
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MATHEMATICA
| Table[EulerPhi[Prime[n + 1] - Prime[n]] - 1, {n, 1, 70}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 30 2006
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PROG
| (MuPAD): for n from 2 to 100 do a := ithprime(n); b := nextprime(a+1); su := 0; for k from a+1 to b-1 do if gcd(k, (b-a)) = 1 then su := su+1; end_if; end_for; print(su); end_for; (Steinerberger)
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CROSSREFS
| Sequence in context: A127537 A025443 A120080 * A060096 A152892 A193002
Adjacent sequences: A111697 A111698 A111699 * A111701 A111702 A111703
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Nov 17 2005
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EXTENSIONS
| More terms from Stefan Steinerberger (hansibal(AT)hotmail.com), Nov 19 2005
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