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A376129
Run lengths of the most significant decimal digit in the primes (A077648).
1
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
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
KEYWORD
nonn,base,new
AUTHOR
Stuart Coe, Sep 11 2024
STATUS
approved