A116516 - OEIS

A116516

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.

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, 8, 7, 5, 1, 4, 4, 7, 5, 1, 3, 2, 3

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OFFSET

1,2

COMMENTS

This constant is similar to Mills's 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 these 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.

LINKS

Table of n, a(n) for n=1..87.

Martin Raab, A prime number "Game of Life": can floor(y*p#) be prime for all p>=2?, arXiv:2403.17949 [math.GM], 2024.

EXAMPLE

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, ...).

CROSSREFS

Sequence in context: A200019 A282824 A106664 * A011417 A231890 A087561

Adjacent sequences: A116513 A116514 A116515 * A116517 A116518 A116519

KEYWORD

nonn,cons

AUTHOR

Martin Raab, Mar 24 2006; extended Apr 22 2006 and again Jun 28 2007

EXTENSIONS

a(76)-a(87) from Jon E. Schoenfield, Jul 23 2017

STATUS

approved