A247025 Lengths of prefixes of the infinite string of digits repeat(1379) that are prime.

2, 3, 7, 81, 223, 250, 255, 537, 543, 1042, 2103, 4285, 25015, 35361, 43525

Offset: 1

Author

Mark E. Shoulson, Sep 09 2014

Keywords

• nonn
• base
• more
• less

Comments

Every prime > 5 in base 10 ends in 1, 3, 7, or 9. If those digits are repeated, in order, some prefixes of that string are prime.

n such that floor(1379/9999 * 10^n) is prime. - Robert Israel, Sep 09 2014

a(13) > 15500. - Daniel Starodubtsev, Mar 16 2021

Examples

			1 and 3 are the first two digits of the string, and 13 is prime. 13 has length 2, so 2 is a term.
137 is prime and three digits long, so 3 is a term.
1379137 is prime and seven digits long, so 7 is a term.
		

Crossrefs

Cf. A000040, A007652.

Programs

Magma

[n: n in [0..300] | IsPrime(Floor(1379/9999 * 10^n))]; // Vincenzo Librandi, Oct 17 2014

Mathematica

Select[Range[4300],PrimeQ[FromDigits[PadRight[{},#,{1,3,7,9}]]]&] (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Jun 11 2024 *)

PARI

lista(nn) = {s = 0; digs = [1,3,7,9]; id = 1; for (n=1, nn, s = 10*s + digs[id]; if (isprime(s), print1(n, ", ")); id++; if (id==5, id = 1););} \\ Michel Marcus, Oct 11 2014

Python

from sympy import isprime
from itertools import cycle
it=cycle([1,3,7,9])
c=0
a=0
for i in it:
    c+=1
    a*=10
    a+=i
    if isprime(a):
        print(c)

Extensions

Edited. Name specified. Example reformulated. a(12) added (using R. Israel's formula). Keyword less and Crossreferences added. - Wolfdieter Lang, Nov 03 2014

a(13)-a(14) from Michael S. Branicky, May 29 2023

a(15) from Michael S. Branicky, Jun 13 2024