A054416 Numbers k such that 9090...9091 (with k-1 copies of 90 and one copy of 91) is prime.

2, 3, 9, 15, 26, 33, 146, 320, 1068, 1505, 134103, 800393

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

Table of n, a(n) for n=1..12.

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

Cf. A001562.

Sequence in context: A061933 A251239 A124881 * A291868 A092638 A206777

Adjacent sequences: A054413 A054414 A054415 * A054417 A054418 A054419

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