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Search: id:A073609
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| A073609 |
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a(0) = 2; a(n) for n > 0 is the smallest prime > a(n-1) that differs from a(n-1) by a square. |
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+0
7
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| 2, 3, 7, 11, 47, 83, 227, 263, 587, 911, 947, 983, 1019, 1163, 1307, 1451, 1487, 1523, 1559, 2459, 3359, 4259, 4583, 5483, 5519, 5843, 5879, 6203, 6779, 7103, 7247, 7283, 7607, 7643, 8219, 8363, 10667, 11243, 11279, 11423, 12323, 12647, 12791, 13367
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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For n > 2, a(n) must be of the form k*36 + 11. This is seen by induction since k*36 + 11 + m^2 is even if m is odd and since k*36 + 11 + (m*6 + 2)^2 and k*36 + 11 + (m*6 + 4)^2 are both divisible by 3. - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Jun 03 2007
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EXAMPLE
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47 differs from 11 by 36 = 6*6 and no prime between 11 and 47 differs from 11 by a square, so 47 is the next term after 11.
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PROGRAM
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(PARI) print1(a=2, ", "); for(n=1, 43, k=1; while(!isprime(b=a+k^2), k++); print1(a=b, ", "))
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CROSSREFS
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Sequence in context: A072534 A056292 A106125 this_sequence A053781 A066749 A046480
Adjacent sequences: A073606 A073607 A073608 this_sequence A073610 A073611 A073612
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 05 2002
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 07 2002
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