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A108739
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Mills' constant A generates a sequence of primes via b(n)=floor(A^3^n). This sequence is a(n) = b(n+1)-b(n)^3.
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2
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3, 30, 6, 80, 12, 450, 894, 3636, 70756, 97220, 66768
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OFFSET
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1,1
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COMMENTS
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This allows larger terms of A051254 (which triple in digits each entry) to be given. Like A051254, currently requires Riemann Hypothesis to show sequence continues.
Currently a(11)=66768 generates only a probable prime number. [Arkadiusz Wesolowski, May 28 2011]
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 8.
W. H. Mills, A prime-representing function, Bull. Amer. Math. Soc., Vol. 53 (1947), page 604.
E. M. Wright, A class of representing functions, J. London Math. Soc., Vol. 29 (1954) pp. 63-71.
Chris K. Caldwell and Yuanyou Cheng, Determining Mills' Constant and a Note on Honaker's Problem, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1.
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LINKS
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Table of n, a(n) for n=1..11.
Chris K. Caldwell, Mills' Theorem - a generalization.
Chris K. Caldwell, The List of Largest Known Primes, The 11th Mills' prime
Chris K. Caldwell and Yuanyou Cheng, Determining Mills' Constant and a Note on Honaker's Problem, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1.
Henri & Renaud Lifchitz, PRP Records
Eric Weisstein's World of Mathematics, Mills' Constant
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FORMULA
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b(1) = 2; b(n+1) = nextprime(b(n)^3); a(n) = b(n+1)-b(n)^3;
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CROSSREFS
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Cf. A051254, A051021.
Sequence in context: A176495 A082792 A078242 * A072973 A154054 A118219
Adjacent sequences: A108736 A108737 A108738 * A108740 A108741 A108742
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KEYWORD
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more,nonn
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AUTHOR
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Chris K. Caldwell (caldwell(AT)utm.edu), Jun 22 2005
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EXTENSIONS
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Three more terms added from Caldwell and Chen, Aug 29 2005
Corrected by T. D. Noe, Sep 24 2008
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STATUS
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approved
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