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A077313 Primes of the form 2^r*5^s - 1. 7

%I

%S 3,7,19,31,79,127,199,499,1249,1279,1999,4999,5119,8191,12799,20479,

%T 31249,49999,51199,79999,81919,131071,199999,524287,799999,1249999,

%U 1310719,3124999,3276799,4999999,7812499,12499999,19999999,20479999

%N Primes of the form 2^r*5^s - 1.

%C 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

%C For n > 1, all terms are congruent to 1 (mod 6). - _Muniru A Asiru_, Sep 29 2017

%H Ray Chandler, <a href="/A077313/b077313.txt">Table of n, a(n) for n = 1..4222</a>

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

%e 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

%t 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 *)

%o (GAP)

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

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

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

%o 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

%Y Cf. A003592, A023509, A077497.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Nov 04 2002

%E More terms from _Reinhard Zumkeller_, Nov 15 2002

%E More terms from _Vladeta Jovovic_, May 08 2003

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)