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Search: id:A008578
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| A008578 |
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Prime numbers at the beginning of the 20th century (today 1 is no longer regarded as a prime). |
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+0
65
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| 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The non-composite numbers.
Also smallest sequence with the property that the product of 2 or more elements with different indices is never a square. - Ulrich Schimke (ulrschimke(AT)aol.com), Dec 12 2001
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 11.
H. D. Huskey, Derrick Henry Lehmer [1905-1991]. IEEE Ann. Hist. Comput. 17 (1995), no. 2, 64-68. Math. Rev. 96b:01035
D. H. Lehmer, The sieve problem for all-purpose computers. Math. Tables and Other Aids to Computation, Math. Tables and Other Aids to Computation, 7, (1953). 6-14. Math. Rev. 14:691e
D. N. Lehmer, "List of Prime Numbers from 1 to 10,006,721", Carnegie Institute, Washington, D.C. 1909.
R. F. Lukes, C. D. Patterson and H. C. Williams, Numerical sieving devices: their history and some applications. Nieuw Arch. Wisk. (4) 13 (1995), no. 1, 113-139. Math. Rev. 96m:11082
Williams, H. C.; Shallit, J. O. Factoring integers before computers. Mathematics of Computation 1943-1993: a half-century of computational mathematics (Vancouver, BC, 1993), 481-531, Proc. Sympos. Appl. Math., 48, AMS, Providence, RI, 1994. Math. Rev. 95m:11143
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
PrimeFan, Arguments for and against the primality of 1.
G. P. Michon, Is 1 a prime number ?
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FORMULA
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m is in the sequence iff sigma(m)+phi(m)=2m. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Jan 27 2005
a(n) = A158611(n+1) for n >= 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jun 19 2009]
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MAPLE
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A008578 := n->if n=1 then 1 else ithprime(i-1);
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MATHEMATICA
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Join[ {1}, Table[ Prime[n], {n, 1, 60} ] ]
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CROSSREFS
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See A000040, which is the main entry for this sequence. The complement of A002808.
Adjacent sequences: A008575 A008576 A008577 this_sequence A008579 A008580 A008581
Sequence in context: A070159 A158611 A000040 this_sequence A100726 A015919 A064555
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KEYWORD
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nonn,easy,nice,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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