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A061106
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Compute Euler totient function for the p(n+1)-p(n)-1 composite numbers between two consecutive primes; choose the smallest.
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2
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2, 2, 4, 4, 6, 6, 8, 8, 8, 12, 16, 12, 20, 16, 18, 16, 20, 24, 24, 24, 32, 24, 24, 40, 32, 48, 36, 40, 32, 48, 40, 44, 48, 40, 48, 54, 80, 48, 56, 48, 60, 64, 84, 60, 48, 72, 96, 72, 88, 72, 64, 80, 72, 84, 80, 72, 88, 96, 92, 96, 80, 120, 96, 144, 80, 96, 108, 112, 120, 116
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 2..1000
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FORMULA
| a(n)=Min{Phi(c) : p(n+1)>c>p(n)}
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EXAMPLE
| p(30)=113 is followed by 13 composites; phi of these are {36, 88, 56, 72, 58, 96, 32, 110, 60, 80, 60, 100, 36}, the smallest of which is 32=a(30) and the largest is 110.
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MATHEMATICA
| Min[EulerPhi[Range[First[#]+1, Last[#]-1]]]&/@Partition[Prime[Range[ 2, 80]], 2, 1] (* From Harvey P. Dale, Aug 18 2011 *)
Table[Min[EulerPhi[Range[Prime[i], Prime[i+1]]]], {i, 2, 100}] (* T. D. Noe, Aug 18 2011 *)
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PROG
| (PARI) { n=-1; q=3; m=10^6; forprime (p=5, prime(1003), a=m; for (i=q + 1, p - 1, a=min(eulerphi(i), a)); q=p; write("b061106.txt", n++, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 18 2009]
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CROSSREFS
| Cf. A000010, A061108.
Sequence in context: A004079 A096494 A116568 * A161764 A131055 A052928
Adjacent sequences: A061103 A061104 A061105 * A061107 A061108 A061109
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), May 29 2001
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