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Search: id:A062395
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| 2, 9, 65, 513, 4097, 32769, 262145, 2097153, 16777217, 134217729, 1073741825, 8589934593, 68719476737, 549755813889, 4398046511105, 35184372088833, 281474976710657, 2251799813685249, 18014398509481985, 144115188075855873
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OFFSET
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0,1
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COMMENT
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Any number of the form b^k+1 is composite for b>2 and k odd since b+1 algebraically divides b^k+1. - Robert G. Wilson v Aug 25 2002.
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REFERENCES
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D. M. Burton, Elementary Number Theory, Allyn and Bacon, Boston, MA, 1976, pp. 51.
G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
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FORMULA
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a(n) = 8a(n-1)-7 = A001018(n)+1 = 9a(n-1) - 8a(n-2).
G.f.: -(-2+9*x)/(-1+x)/(-1+8*x). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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MAPLE
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with(finance):seq(mul(cashflows([2, 2, 4], 0 ), k=1..n)+1, n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
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MATHEMATICA
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Table[8^n + 1, {n, 0, 20}]
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PROGRAM
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(PARI) for(n=0, 22, print(8^n+1)).
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CROSSREFS
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Cf. A054977, A007395, A000051, A034472, A052539, A034474, A062394, A034491, A062396, A062397, A007689, A063376, A063481, A074600 - A074624, A034524 for numbers one more than powers.
Sequence in context: A038038 A048801 A071300 this_sequence A099975 A127056 A042255
Adjacent sequences: A062392 A062393 A062394 this_sequence A062396 A062397 A062398
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 22 2001
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