cp's OEIS Frontend

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

%I A077313 #21 Sep 30 2017 23:47:47
%S A077313 3,7,19,31,79,127,199,499,1249,1279,1999,4999,5119,8191,12799,20479,
%T A077313 31249,49999,51199,79999,81919,131071,199999,524287,799999,1249999,
%U A077313 1310719,3124999,3276799,4999999,7812499,12499999,19999999,20479999
%N A077313 Primes of the form 2^r*5^s - 1.
%C A077313 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 A077313 For n > 1, all terms are congruent to 1 (mod 6). - _Muniru A Asiru_, Sep 29 2017
%H A077313 Ray Chandler, <a href="/A077313/b077313.txt">Table of n, a(n) for n = 1..4222</a>
%e A077313 1250000 = 2*2*2*2*5*5*5*5*5*5*5 and 1250000 - 1 = A000040(96469), therefore 1249999 is a term.
%e A077313 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 A077313 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 A077313 (GAP)
%o A077313 A:=Filtered([1..10^7],IsPrime);;    I:=[5];;
%o A077313 B:=List(A,i->Elements(Factors(i+1)));;
%o A077313 C:=List([0..Length(I)],j->List(Combinations(I,j),i->Concatenation([2],i)));;
%o A077313 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 A077313 Cf. A003592, A023509, A077497.
%K A077313 nonn
%O A077313 1,1
%A A077313 _Amarnath Murthy_, Nov 04 2002
%E A077313 More terms from _Reinhard Zumkeller_, Nov 15 2002
%E A077313 More terms from _Vladeta Jovovic_, May 08 2003