OFFSET
1,1
COMMENTS
Numbers k such that 10*(10^(2k)-1)/11 + 1 is prime.
REFERENCES
J. A. H. Hunter and J. S. Madachy, Mathematical Diversions, New York: Dover Publications, Inc., 1974, pp. 4-5. Originally published by Van Nostrand, 1963.
LINKS
David Broadhurst, Proof that 1505 term is prime [BROKEN LINK]
David Broadhurst, Unique record, digest of 3 messages in primenumbers Yahoo group, Apr 8-9, 2001. [Cached copy]
FORMULA
a(n) = (A001562(n)-1)/2.
EXAMPLE
The first 3 numbers are 9091, 909091, 909090909090909091.
MATHEMATICA
Do[ If[ PrimeQ[ 10*(10^(2n) - 1)/11 + 1], Print[ n ] ], {n, 0, 1505} ]
Position[Table[FromDigits[PadLeft[{9, 1}, 2n, {9, 0}]], {n, 1510}], _?PrimeQ]// Flatten (* Harvey P. Dale, Nov 02 2017 *)
PROG
(Python)
from sympy import isprime, prime
def afind(limit, startk=1):
s = "90"*(startk-1)
for k in range(startk, limit+1):
if isprime(int(s+"91")):
print(k, end=", ")
s += "90"
afind(400) # Michael S. Branicky, Jan 13 2022
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), May 22 2000
EXTENSIONS
More terms from Michael Kleber and Harvey Dubner (harvey(AT)dubner.com), May 22 2000
Ignacio Larrosa Cañestro reports that the 1068 term has now been established to be a prime using Titanix 1.01, Oct 23 2000
a(11)-a(12) from Michael S. Branicky, Jan 13 2022 using A001562
STATUS
approved