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A065966
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Numbers n such that phi(n) / 2 is prime.
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10
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5, 7, 8, 9, 10, 11, 12, 14, 18, 22, 23, 46, 47, 59, 83, 94, 107, 118, 166, 167, 179, 214, 227, 263, 334, 347, 358, 359, 383, 454, 467, 479, 503, 526, 563, 587, 694, 718, 719, 766, 839, 863, 887, 934, 958, 983, 1006, 1019, 1126, 1174, 1187, 1283, 1307, 1319
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is probably an infinite sequence, but a proof would be nice. Are there infinitely many consecutive terms of the sequence which are also consecutive integers? (For example, 7, 8 and 46, 47.)
Apart from 8, 9, 12 and 18, all the terms of the sequence are safe primes or twice safe primes. It is not known if there are infinitely many safe primes (cf. A005385, A005384). For consecutive terms of the sequence which are also consecutive integers see A066179. - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 16 2001
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| Numbers n such that A068212(n)=2
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EXAMPLE
| phi(46)/2 = 22/2 = 11, a prime.
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PROG
| (PARI) for(n=3, 5000, if(isprime(eulerphi(n)/2), print1(n, ", ")))
(PARI) { n=0; for (m=3, 10^9, if (isprime(eulerphi(m)/2), write("b065966.txt", n++, " ", m); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 05 2009]
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CROSSREFS
| Cf. A000010, A005385, A005384, A066179, A006530, A052126, A068211, A068212.
Sequence in context: A068001 A191846 A068213 * A096989 A031950 A043694
Adjacent sequences: A065963 A065964 A065965 * A065967 A065968 A065969
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 08 2001
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EXTENSIONS
| More terms from Jason Earls (zevi_35711(AT)yahoo.com), Dec 09 2001
Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Mar 18 2010
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