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Search: id:A109472
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| A109472 |
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Cumulative sum of primes p such that 2^p - 1 is a Mersenne prime. |
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1
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| 2, 5, 10, 17, 30, 47, 66, 97, 158, 247, 354, 481, 1002, 1609, 2888, 5091, 7372, 10589, 14842, 19265, 28954, 38895, 50108, 70045, 91746, 114955, 159452, 245695, 356198, 488247, 704338, 1461177, 2320610, 3578397, 4976666, 7952887, 10974264
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OFFSET
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1,1
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COMMENT
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Prime cumulative sum of primes p such that 2^p - 1 is a Mersenne prime include: a(1) = 2, a(2) = 5, a(4) = 17, a(6) = 47, a(8) = 97, a(14) = 1609, a(18) = 10589. After 1, all such indices x of prime a(x) must be even.
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FORMULA
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a(n) = SUM[from i = 0 to n] A000043(i).
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EXAMPLE
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a(1) = 2, since 2^2-1 = 3 is a Mersenne prime.
a(2) = 2 + 3 = 5, since 2^3-1 = 7 is a Mersenne prime.
a(3) = 2 + 3 + 5 = 10, since 2^5-1 = 31 is a Mersenne prime.
a(4) = 2 + 3 + 5 + 7 = 17, since 2^7-1 = 127 is a Mersenne prime; 17 itself is prime (in fact a p such that 2^p-1 is a Mersenne prime).
a(18) = 2+3+5+7+13+17+19+31+61+89+107+127+521+607+1279+2203+2281+3217 = 10589 (which is prime).
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CROSSREFS
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Cf. A000043, A000668 for the Mersenne primes, A001348, A046051, A057951-A057958.
Sequence in context: A071602 A046485 A109377 this_sequence A146268 A038358 A107482
Adjacent sequences: A109469 A109470 A109471 this_sequence A109473 A109474 A109475
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 28 2005
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