A255311 Decimal expansion of the prime gap constant (concatenate the sizes of prime gaps, A001223).

1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 1, 4, 4, 6, 2, 1, 0, 2, 6, 6, 4, 6, 6, 2, 1, 0, 2, 4, 2, 1, 2, 1, 2, 4, 2, 4, 6, 2, 1, 0, 6, 6, 6, 2, 6, 4, 2, 1, 0, 1, 4, 4, 2, 4, 1, 4, 6, 1, 0, 2, 4, 6, 8, 6, 6, 4, 6, 8, 4, 8, 1, 0, 2, 1, 0, 2, 6, 4, 6, 8, 4, 2, 4, 1, 2, 8, 4, 8, 4, 6, 1, 2, 2, 1, 8, 6, 1, 0, 6, 6, 2, 6, 1, 0, 6, 6, 2, 6

Offset

1,2

Comments

This prime gap constant is similar in spirit to the Copeland-Erdős constant (A033308) and to the Champernowne constant (A033307). Its fractional part, the digits of which represent this sequence, is given as the limit of concatenating the digits (A255307) in the size of gaps between consecutive primes (A001223), while its integer part is zero by definition, as is the case with the other two constants.

The two other constants mentioned above are concatenation of strictly increasing numbers, which might be considered as a significant difference. At least at the beginning of this sequence, odd digits are quite rare, especially the larger ones. (The first digit '9' occurs at index n=46634.) Although prime gaps tend to increase, it is questionable whether this constant is normal, since it may be conjectured (generalizing the twin prime conjecture) that all (and especially small) gaps occur infinitely often. - M. F. Hasler, Apr 08 2015

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

Example of the value of this constant for the first 100 digits in the fractional part of its digital expansion: 0.122424246264246626426468424241446210266466210242121242462106662642101442...

Mathematica

Flatten[IntegerDigits[Table[Prime[n+1]- Prime[n], {n, 1, 100}]]]
Flatten[IntegerDigits/@Differences[Prime[Range[200]]]] (* Harvey P. Dale, Jan 30 2019 *)

Prog

(PARI) print1("0."); forprime(p=1+o=2, 360749, print1(-o+o=p)) \\ M. F. Hasler, Apr 08 2015

Crossrefs

Cf. A001223, A255307, A033307, A033308.

Sequence in context: A303809 A193562 A249868 * A075526 A001223 A118776

Adjacent sequences: A255308 A255309 A255310 * A255312 A255313 A255314

Keyword

nonn,base,cons

Author

Waldemar Puszkarz, Feb 20 2015

Status

approved