cp's OEIS Frontend

A386495 Least prime starting a sequence of exactly n consecutive primes with identical counts of even digits.

%I A386495 #41 Aug 04 2025 19:49:56
%S A386495 2,17,13,11,7,5,3,491,14303,14293,157259,157253,1525723,4576997,
%T A386495 4576993,4576991,10411013,33388093,188332121,194259301,2853982501,
%U A386495 2853982499,2853982477,3913474277,10883385143,22809734971,34883348389,34883348369,34883348341,742012786121
%N A386495 Least prime starting a sequence of exactly n consecutive primes with identical counts of even digits.
%C A386495 Consecutive previous primes of the selected prime are ignored even though the may also have an identical count of digits.
%H A386495 David A. Corneth, <a href="/A386495/a386495.gp.txt">PARI program</a>
%e A386495 a(2) = 17, because the two primes in the sequence starting at  — namely [17, 19] — each contain the same number of even digits, and no earlier prime sequence meets this criterion.
%e A386495 n In [a(n), ...]
%e A386495 1 In [2], each of the 1 number contain 1 even digit.
%e A386495 2 In [17, 19], each of the 2 numbers contains 0 even digit.
%e A386495 3 In [13, 17, 19], each of the 3 numbers contains 0 even digit.
%e A386495 4 In [11, 13, 17, 19], each of the 4 numbers contains 0 even digit.
%e A386495 5 In [7, 11, 13, 17, 19], each of the 5 numbers contains 0 even digit.
%e A386495 6 In [5, 7, 11, 13, 17, 19], each of the 6 numbers contains 0 even digit.
%e A386495 7 In [3, 5, 7, 11, 13, 17, 19], each of the 7 numbers contains 0 even digit.
%e A386495 8 In [491, 499, 503, 509, 521, 523, 541, 547], each of the 8 numbers contains 1 even digit.
%e A386495 9 In [14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389], each of the 9 numbers contains 2 even digits.
%e A386495 10 In [14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389], each of the 10 numbers contains 2 even digits.
%e A386495 11 In [157259, 157271, 157273, 157277, 157279, 157291, 157303, 157307, 157321, 157327, 157349], each of the 11 numbers contains 1 even digit.
%e A386495 12 In [157253, 157259, 157271, 157273, 157277, 157279, 157291, 157303, 157307, 157321, 157327, 157349], each of the 12 numbers contains 1 even digit.
%o A386495 (PARI) \\ See Corneth link
%o A386495 (PARI)
%o A386495 card(p)={my(c=0,u=digits(p),n=sum(i=1,#u,u[i]%2==0),even=n);while(even==n,p=nextprime(p+1);u=digits(p);even=sum(i=1,#u,u[i]%2==0);c++);c}
%o A386495 data(pp=10^9)={my(u=vector(30),r=0);forprime(p=2,pp,my(n=card(p));if(u[n]==0,u[n]=p;if(n>r,r=n)));u[1..r]}
%Y A386495 Cf. A196563, A386475.
%K A386495 nonn,base
%O A386495 1,1
%A A386495 _Jean-Marc Rebert_, Jul 23 2025
%E A386495 a(19)-a(20) from _David A. Corneth_, Jul 23 2025
%E A386495 a(21)-a(26) from _Jean-Marc Rebert_, Jul 24 2025
%E A386495 a(27)-a(30) from _Giovanni Resta_, Jul 24 2025