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Search: id:A114409
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| A114409 |
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Length of all-prime chain of prime[n] + successive even pentagonal numbers. |
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+0
1
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| 1, 2, 3, 2, 1, 2, 4, 1, 2, 4, 1, 2, 1, 2, 1, 2, 4, 4, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 5, 1, 2, 2, 1, 3, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 4, 1, 2
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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a(1) is undefined, as prime(1) is the only even prime, for which the length-5 chain is of 2 + successive odd pentagonal numbers A014632: 2 prime, 2+1 = 3 prime, 2+5 = 7 prime, 2+35 = 37 prime, 2+51 = 53 prime, but 2+117 = 119 = 7 * 17 nonprime. Pentagonal numbers A000326 = n*(3*n-1)/2 = 0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ... Even pentagonal numbers A014633 = 12, 22, 70, 92, 176, 210, 330, 376, 532, 590, 782, 852, 1080, ...
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FORMULA
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a(n) = k = length of chain prime[n] + A014633(1) + ... + A014633(k) such that each term in the chain is prime.
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EXAMPLE
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a(2) = 1 because prime(2) = 3 is prime, but prime(2) + EvenPent(1) = 3 + 12 = 15 = 3 * 5 is nonprime, giving a chain of just 1 successive prime.
a(3) = 2 because 5 is prime, prime(3) + EvenPent(1) = 5 + 12 = 17 is prime, but prime(3) + EvenPent(2) = 5 + 22 = 27 = 3^3 is nonprime, giving a chain of 2 successive primes.
a(4) = 3 because 7 is prime, 7+12 = 19 is prime, 7+22 = 29 is prime, but 7+70 = 77 = 7*11 is nonprime, for a chain of 3 successive primes.
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CROSSREFS
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Cf. A000040, A000326, A014633.
Sequence in context: A058207 A105969 A163530 this_sequence A049063 A120894 A134819
Adjacent sequences: A114406 A114407 A114408 this_sequence A114410 A114411 A114412
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 11 2006
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