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Search: id:A065966
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| A065966 |
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Numbers n such that EulerPhi(n) / 2 is prime. |
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8
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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; listen)
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OFFSET
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1,1
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COMMENT
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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
phi(n)=semiprime (or biprime). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 29 2009]
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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Numbers n such that A068212(n)=2
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EXAMPLE
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EulerPhi(46)/2 = 22/2 = 11, a prime.
A000010(a(n))=semiprime. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 29 2009]
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PROGRAM
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(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
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Cf. A000010, A005385, A005384, A066179, A006530, A052126, A068211, A068212.
Cf. A001358 (semiprimes orbiprimes). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 29 2009]
Sequence in context: A141606 A068001 A068213 this_sequence A096989 A031950 A043694
Adjacent sequences: A065963 A065964 A065965 this_sequence A065967 A065968 A065969
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 08 2001
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EXTENSIONS
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More terms from Jason Earls (zevi_35711(AT)yahoo.com), Dec 09 2001
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