A386495 Least prime starting a sequence of exactly n consecutive primes with identical counts of even digits.
2, 17, 13, 11, 7, 5, 3, 491, 14303, 14293, 157259, 157253, 1525723, 4576997, 4576993, 4576991, 10411013, 33388093, 188332121, 194259301, 2853982501, 2853982499, 2853982477, 3913474277, 10883385143, 22809734971, 34883348389, 34883348369, 34883348341, 742012786121
Offset: 1
Examples
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. n In [a(n), ...] 1 In [2], each of the 1 number contain 1 even digit. 2 In [17, 19], each of the 2 numbers contains 0 even digit. 3 In [13, 17, 19], each of the 3 numbers contains 0 even digit. 4 In [11, 13, 17, 19], each of the 4 numbers contains 0 even digit. 5 In [7, 11, 13, 17, 19], each of the 5 numbers contains 0 even digit. 6 In [5, 7, 11, 13, 17, 19], each of the 6 numbers contains 0 even digit. 7 In [3, 5, 7, 11, 13, 17, 19], each of the 7 numbers contains 0 even digit. 8 In [491, 499, 503, 509, 521, 523, 541, 547], each of the 8 numbers contains 1 even digit. 9 In [14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389], each of the 9 numbers contains 2 even digits. 10 In [14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389], each of the 10 numbers contains 2 even digits. 11 In [157259, 157271, 157273, 157277, 157279, 157291, 157303, 157307, 157321, 157327, 157349], each of the 11 numbers contains 1 even digit. 12 In [157253, 157259, 157271, 157273, 157277, 157279, 157291, 157303, 157307, 157321, 157327, 157349], each of the 12 numbers contains 1 even digit.
Links
- David A. Corneth, PARI program
Programs
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PARI
\\ See Corneth link
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PARI
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} 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]}
Extensions
a(19)-a(20) from David A. Corneth, Jul 23 2025
a(21)-a(26) from Jean-Marc Rebert, Jul 24 2025
a(27)-a(30) from Giovanni Resta, Jul 24 2025
Comments