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Search: id:A116516
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| A116516 |
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Decimal expansion of constant C such that Floor[p#*C] is always a prime number (for p>=2), where p# is the primorial-function, i.e. the product of prime numbers up to and including p. |
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+0
2
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| 1, 2, 5, 4, 1, 9, 6, 1, 0, 1, 5, 7, 8, 0, 1, 1, 9, 3, 6, 2, 7, 7, 6, 7, 9, 5, 5, 4, 9, 1, 4, 2, 1, 3, 4, 2, 3, 7, 7, 9, 8, 6, 9, 2, 1, 8, 0, 4, 2, 6, 2, 2, 1, 9, 5, 8, 3, 2, 7, 2, 2, 5, 5, 4, 6, 0, 8, 8, 6, 4, 6, 9, 9, 4, 2
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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This constant is similar to the Mills' constant (where floor[x^(3^n)] is always prime). I've calculated it all by myself, and I never heard of it before. I can't even prove that it exists, but after my calculations, it is most likely. It definitely starts with this 43 decimal digits. Does anybody know if anyone calculated this before?
There should be infinitely many constants such that Floor[p#*C] is always prime, but the range in which these numbers appear is extremely narrow, and every such constant would start with these 74 decimal digits.
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EXAMPLE
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If the constant 1.2541961... is continuously multiplied by the prime numbers 2, 3, 5, 7, 11 ..., then floor[x] is always prime (i.e. 2, 7, 37, 263, 2897...).
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CROSSREFS
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Sequence in context: A106315 A100946 A106664 this_sequence A011417 A087561 A009738
Adjacent sequences: A116513 A116514 A116515 this_sequence A116517 A116518 A116519
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KEYWORD
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nonn,cons
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AUTHOR
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Martin Raab (raab-martin(AT)gmx.de), Mar 24 2006; extended Apr 22 2006 and again Jun 28 2007
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