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A059864 Product_{i=4..n} (p(i)-5), where p(i) is i-th prime. +0
1
1, 1, 1, 2, 12, 96, 1152, 16128, 290304, 6967296, 181149696, 5796790272, 208684449792, 7930009092096, 333060381868032, 15986898329665536, 863292509801938944, 48344380548908580864, 2997351594032332013568 (list; graph; listen)
OFFSET

1,4

COMMENT

Such products arise in Hardy-Littlewood prime k-tuplet conjectural formulas.

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 84-94.

R. K. Guy, Unsolved Problems in Number Theory, A8, A1

G. H. Hardy and J. E. Littlewood, "Partitio Numerorum III", Acta Math. 44 (1922) 1-70.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979.

G. Polya, Mathematics and Plausible Reasoning, Vol. II, Appendix Princeton UP, 1954

G. Polya, Heuristic reasoning in the theory of numbers, Am. Math. Monthly,66 (1959), 375-384.

LINKS

C. K. Caldwell, Prime k-tuple Conjecture

S. R. Finch, Hardy-Littlewood Constants

G. Niklasch, Some number theoretical constants: 1000-digit values

CROSSREFS

Cf. A049296, A002110, A005867, A000847, A022008, A051160-A051168, A048298, A059861-A059865.

Sequence in context: A014297 A052564 A052611 this_sequence A095338 A012548 A012550

Adjacent sequences: A059861 A059862 A059863 this_sequence A059865 A059866 A059867

KEYWORD

nonn

AUTHOR

Labos E. (labos(AT)ana.sote.hu), Feb 28 2001

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


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