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Search: id:A001771
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| A001771 |
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Numbers n such that 7*2^n - 1 is prime.
(Formerly M3784 N1541)
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+0
14
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| 1, 5, 9, 17, 21, 29, 45, 177, 18381, 22529, 24557, 26109, 34857, 41957, 67421, 70209, 169085, 173489, 177977, 363929, 372897
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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n is always of the form 4*k + 1
If n is in the sequence and m=2^(n+2)*3*(7*2^n-1) then phi(m)+sigma(m)=3m (m is in the sequence A011251). The proof is easy. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Mar 04 2005
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REFERENCES
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H. Riesel, ``Prime numbers and computer methods for factorization,'' Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384.
H. C. Williams and C. R. Zarnke, Math. Comp., 22 (1968), 420-422.
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LINKS
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Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime
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MATHEMATICA
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Do[ If[ PrimeQ[7*2^n - 1], Print[n]], {n, 1, 2500}]
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PROGRAM
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(PARI) v=[ ]; for(n=0, 2000, if(isprime(7*2^n-1), v=concat(v, n), )); v
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CROSSREFS
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Cf. A050523, A003307, A002235, A046865, A079906, A046866, A005541, A056725, A046867, A079907.
Cf. A032353, 7*2^n+1 is prime.
Sequence in context: A062777 A102179 A097538 this_sequence A022341 A095725 A005006
Adjacent sequences: A001768 A001769 A001770 this_sequence A001772 A001773 A001774
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KEYWORD
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hard,nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from Douglas Burke (dburke(AT)nevada.edu).
More terms from Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 23 2004
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