A213790 -id:A213790 - cp's OEIS frontend

A213883 Least number k such that (10^k-j)*10^n-1 is prime for some single-digit j or 0 if no such prime with 1<=k, 0<=j<=9 exists.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 1, 3, 5, 5, 3, 1, 3, 3, 1, 1, 9, 1, 1, 1, 1, 1, 7, 3, 6, 4, 1, 4, 4, 1, 15, 10, 1, 7, 3, 1, 3, 2, 2, 4, 6, 1, 3, 5, 20, 1, 1, 1, 8, 10, 7, 15, 10, 1, 4, 2, 5, 8, 3, 23, 11, 2, 2, 9, 3, 1, 5, 4, 1, 6, 3, 18, 2

Offset: 1

Pierre CAMI, Jun 26 2012

nonn

j cannot be 0, 3, 6 or 9 because we are searching for repdigit primes with k-1 times the digit 9, one digit (9-j), and n least-significant digits 9 (so n+k-1 times the digit 9 in total). If j is a multiple of 3, that number is also a multiple of 3 and not prime.

Conjecture: there is always at least one (k,j) solution for each n.

			Refers to the primes 89, 599, 8999, 79999, 799999, 4999999, 89999999,...

Pierre CAMI, Table of n, a(n) for n = 1..2200

Cf. A213790, A213884 (corresponding j).

A213883 := proc(n)
    for k from 1 to 2*n-1 do
        for j from 0 to 9 do
            if isprime( (10^k-j)*10^n-1) then
                return k;
            end if;
        end do:
    end do:
    return 0 ;
end proc: # R. J. Mathar, Jul 20 2012

A214795 a(n) is the smallest k>=2 such that n divides Fibonacci(k-1)+21.

Original entry on oeis.org

2, 2, 5, 5, 10, 5, 9, 5, 17, 12, 2, 5, 6, 9, 13, 17, 8, 17, 11, 53, 9, 2, 4, 5, 30, 6, 45, 17, 7, 33, 23, 41, 13, 8, 33, 17, 47, 11, 21, 53, 29, 9, 53, 23, 93, 33, 25, 17, 65, 30, 29, 23, 42, 45, 10, 17, 29, 21, 51, 53

Offset: 1

Art DuPre, Aug 03 2012

nonn

The n-th entry a(n) means that a(n) is the index of the first term in A000045+21 which n divides.

Cf. A214789, A213790, A214791, A214792

skdf[n_]:=Module[{k=2},While[!Divisible[Fibonacci[k-1]+21,n],k++];k]; Array[ skdf,60] (* Harvey P. Dale, Nov 25 2017 *)

Definition corrected. - R. J. Mathar, Aug 09 2012

A228144 Smallest k > n such that j10^k + m10^n - 1 is a prime number for at least a pair {j,m} with 0 < j < 10 and 0 < m < 10.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 46, 47, 48, 49, 50, 51, 52, 53, 55, 55, 56, 57, 59, 59, 60, 61, 62, 63, 64, 66, 66, 67, 68, 70

Offset: 1

Pierre CAMI, Aug 14 2013

nonn

The prime numbers are the sum of a near repdigit number starting with the digit j followed by k digits 0 and a nearepdigit number starting with the digit (m-1) followed by n digits 9 for m>1, or for m=1 a repdigit number with n digits 9.
The first primes are :
109, 1399, 13999, 139999, 1199999, 16999999, 289999999, 2099999999, 10999999999, 239999999999, 1099999999999, 34999999999999, 349999999999999, 2399999999999999.
Conjecture: there is always at least one k for each n.

			1*10^1+1*10^2=109 prime so a(1)=2.

Pierre CAMI, Table of n, a(n) for n = 1..4000

Cf. A213790, A213883.

cp's OEIS Frontend

A213883 Least number k such that (10^k-j)*10^n-1 is prime for some single-digit j or 0 if no such prime with 1<=k, 0<=j<=9 exists.

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A214795 a(n) is the smallest k>=2 such that n divides Fibonacci(k-1)+21.

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A228144 Smallest k > n such that j10^k + m10^n - 1 is a prime number for at least a pair {j,m} with 0 < j < 10 and 0 < m < 10.

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cp's OEIS Frontend

A213883 Least number k such that (10^k-j)*10^n-1 is prime for some single-digit j or 0 if no such prime with 1<=k, 0<=j<=9 exists.

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Author

Keywords

Comments

Examples

Links

Crossrefs

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Maple

A214795 a(n) is the smallest k>=2 such that n divides Fibonacci(k-1)+21.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Extensions

A228144 Smallest k > n such that j*10^k + m*10^n - 1 is a prime number for at least a pair {j,m} with 0 < j < 10 and 0 < m < 10.

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A228144 Smallest k > n such that j10^k + m10^n - 1 is a prime number for at least a pair {j,m} with 0 < j < 10 and 0 < m < 10.