A376129 Run lengths of the most significant decimal digit in the primes (A077648).

1, 1, 1, 1, 4, 2, 2, 3, 2, 2, 3, 2, 1, 21, 16, 16, 17, 14, 16, 14, 15, 14, 135, 127, 120, 119, 114, 117, 107, 110, 112, 1033, 983, 958, 930, 924, 878, 902, 876, 879, 8392, 8013, 7863, 7678, 7560, 7445, 7408, 7323, 7224, 70435, 67883, 66330, 65367, 64336, 63799, 63129, 62712, 62090

Offset

1,5

Links

Table of n, a(n) for n=1..58.

Formula

a(n) = A000720(A037124(n+6)) - A000720(A037124(n+5)) for n >= 5. - Pontus von Brömssen, Oct 07 2024

Example

The primes and the run lengths of their initial digits begin
  primes   2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...
  runs                 \------------/  \----/  \----/
  lengths  1  1  1  1         4          2       2     ...

Prog

(Python)
from sympy import primepi
def A376129(n):
    if n<5: return 1
    def f(m): return (lambda x:primepi(10**x[0]*(x[1]+1)))(divmod(m, 9))
    return int(f(n+5)-f(n+4)) # Chai Wah Wu, Oct 16 2024

Crossrefs

Cf. A000720, A037124, A077648.

Sequence in context: A058634 A037919 A049849 * A112349 A231821 A062072

Adjacent sequences: A376126 A376127 A376128 * A376130 A376131 A376132

Keyword

nonn,base

Author

Stuart Coe, Sep 11 2024

Status

approved