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Search: id:A132403
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| A132403 |
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Analogue of Pascal's triangle, but with "next prime" applied to each sum. |
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+0
1
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| 1, 2, 2, 3, 5, 3, 5, 11, 11, 5, 7, 17, 23, 17, 7, 11, 29, 41, 41, 29, 11, 13, 41, 71, 83, 71, 41, 13, 17, 59, 113, 157, 157, 113, 59, 17, 19, 79, 173, 271, 317, 271, 173, 79, 19, 23, 101, 257, 449, 593, 593, 449, 257, 101, 23, 29, 127, 359, 709, 1049, 1187, 1049, 709, 359
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Each number is the smallest prime => the sum of the 2 numbers above (consider each line padded with 0 on each side).
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FORMULA
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Array read by rows: A[k+1,n] = nextprime(A[k,n] + A[k,n+1]) = A007918(A[k,n] + A[k,n+1]).
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EXAMPLE
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Triangle begins:
1
2....2
3....5....3
5...11...11....5
7...17...23...17....7
11..29...41...41...29...11
13..41...71...83...71...41...13
17..59..113..157..157..113...59...17
19..79..173..271..317..271..173...79...19
23.101..257..449..593..593..449..257..101...23
29.127..359..709.1049.1187.1049..709..359..127..29
31.157..487.1069.1759.2237.2237.1759.1069..487.157..31
37.191..647.1559.2833.4001.4583.4001.2833.1559.647.191.37.
First column is primes A000040. Second column is A064337. Analogue of central binomial coefficient A000984 is the central numbers in this triangle, beginning: 1, 5, 23, 83, 317, 1187, 4583, 17327. Different triangles result if the 1st row is a pair other than (2,2). Asymmetric triangles occur if the 1st row consists of unequal integers.
The number under the middle of the row (2, 2) is 5 because 5 is smallest prime equal to or greater than 2+2 = 4.
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CROSSREFS
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Cf. A000040, A000984, A007918, A007308, A064337.
Sequence in context: A125101 A047666 A067330 this_sequence A113167 A036014 A076228
Adjacent sequences: A132400 A132401 A132402 this_sequence A132404 A132405 A132406
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 12 2007
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