login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A077313 Primes of the form 2^r*5^s - 1. 7
3, 7, 19, 31, 79, 127, 199, 499, 1249, 1279, 1999, 4999, 5119, 8191, 12799, 20479, 31249, 49999, 51199, 79999, 81919, 131071, 199999, 524287, 799999, 1249999, 1310719, 3124999, 3276799, 4999999, 7812499, 12499999, 19999999, 20479999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p such that 10^p is divisible by p+1. Primes p whose fractions p/(p+1) are terminating decimals, i.e., primes p such that A158911(p)=0. Primes p such that the prime divisors of p+1 are also prime divisors of the numbers m obtained by the concatenation of p and p+1. For example, for p=19, m = 1920, the prime divisors of 20 are {2, 5} and the prime divisors of 1920 are {2, 3, 5}. - Jaroslav Krizek, Feb 25 2013

For n > 1, all terms are congruent to 1 (mod 6). - Muniru A Asiru, Sep 29 2017

LINKS

Ray Chandler, Table of n, a(n) for n = 1..4222

EXAMPLE

1250000 = 2*2*2*2*5*5*5*5*5*5*5 and 1250000 - 1 = A000040(96469), therefore 1249999 is a term.

List of (r, s): (2, 0), (3, 0), (2, 1), (5, 0), (4, 1), (7, 0), (3, 2), (2, 3), (1, 4), (8, 1), (4, 3), (3, 4), (10, 1), ...  - Muniru A Asiru, Sep 29 2017

MATHEMATICA

With[{n = 10^8}, Union@ Select[Flatten@ Table[2^p*5^q - 1, {p, 0, Log[2, n/(1)]}, {q, 0, Log[5, n/(2^p)]}], PrimeQ]] (* Michael De Vlieger, Sep 30 2017 *)

PROG

(GAP)

A:=Filtered([1..10^7], IsPrime);;    I:=[5];;

B:=List(A, i->Elements(Factors(i+1)));;

C:=List([0..Length(I)], j->List(Combinations(I, j), i->Concatenation([2], i)));;

A077313:=List(Set(Flat(List([1..Length(C)], i->List([1..Length(C[i])], j->Positions(B, C[i][j]))))), i->A[i]); # Muniru A Asiru, Sep 29 2017

CROSSREFS

Cf. A003592, A023509, A077497.

Sequence in context: A141173 A145472 A217199 * A102271 A145039 A112633

Adjacent sequences:  A077310 A077311 A077312 * A077314 A077315 A077316

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Nov 04 2002

EXTENSIONS

More terms from Reinhard Zumkeller, Nov 15 2002

More terms from Vladeta Jovovic, May 08 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 20 23:22 EDT 2019. Contains 321354 sequences. (Running on oeis4.)