This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376129 #16 Oct 16 2024 22:26:37 %S A376129 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, %T A376129 114,117,107,110,112,1033,983,958,930,924,878,902,876,879,8392,8013, %U A376129 7863,7678,7560,7445,7408,7323,7224,70435,67883,66330,65367,64336,63799,63129,62712,62090 %N A376129 Run lengths of the most significant decimal digit in the primes (A077648). %F A376129 a(n) = A000720(A037124(n+6)) - A000720(A037124(n+5)) for n >= 5. - _Pontus von Brömssen_, Oct 07 2024 %e A376129 The primes and the run lengths of their initial digits begin %e A376129 primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ... %e A376129 runs \------------/ \----/ \----/ %e A376129 lengths 1 1 1 1 4 2 2 ... %o A376129 (Python) %o A376129 from sympy import primepi %o A376129 def A376129(n): %o A376129 if n<5: return 1 %o A376129 def f(m): return (lambda x:primepi(10**x[0]*(x[1]+1)))(divmod(m,9)) %o A376129 return int(f(n+5)-f(n+4)) # _Chai Wah Wu_, Oct 16 2024 %Y A376129 Cf. A000720, A037124, A077648. %K A376129 nonn,base %O A376129 1,5 %A A376129 _Stuart Coe_, Sep 11 2024