cp's OEIS Frontend

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.

A065683 Number of primes <= prime(n) which begin with a 4.

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%I A065683 #17 Dec 15 2024 11:01:26
%S A065683 0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%T A065683 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%U A065683 3,3,3,3,3,3,3,3,3,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,20,20,20
%N A065683 Number of primes <= prime(n) which begin with a 4.
%H A065683 Harry J. Smith, <a href="/A065683/b065683.txt">Table of n, a(n) for n = 1..1000</a>
%e A065683 41 = A000040(13) is the first prime beginning with 4, so a(13) = 1. a(664579) = 74114 (A000040(664579) = 9999991 is the largest prime < 10^7).
%t A065683 Table[Count[Take[Prime[Range[100]],n],_?(First[IntegerDigits[#]] == 4&)],{n,100}]  (* _Harvey P. Dale_, Apr 18 2011 *)
%o A065683 (PARI) lista(n) = { my(a=[p\10^logint(p,10)==4 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ _Harry J. Smith_, Oct 26 2009
%Y A065683 Cf. A000040, A045710, A065680.
%K A065683 base,nonn
%O A065683 1,14
%A A065683 _Reinhard Zumkeller_, Nov 13 2001