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A077313
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Primes of the form 2^r*5^s - 1.
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7
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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