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Search: id:A167276
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| A167276 |
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Primes p such that p^2=x^2+y^2-1 with x and y also prime. |
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+0
1
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| 7, 13, 17, 23, 31, 37, 41, 43, 47, 53, 67, 73, 83, 89, 103, 107, 109, 137, 149, 151, 157, 163, 173, 191, 193, 227, 229, 233, 241, 263, 269, 293, 307, 311, 313, 317, 331, 337, 353, 359, 383, 389, 397, 401, 421, 431, 439, 443, 457, 463, 467, 487, 499, 523, 557, 577, 593, 599, 613, 619, 643, 683, 701, 727, 733, 757, 773, 829, 839, 853, 857, 863, 887, 947, 967, 977, 983, 997
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Appears to be infinite.
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FORMULA
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{ A000040(i): A066872(i) in A045636}. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 09 2009]
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EXAMPLE
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a(1)=7 (x=5, y=5); a(2)=13 (x=7, y=11); a(3)=17 (x=11, y=17); a(4)=23 (x=13, y=19); a(5)=31 (x=11, y=31);...; a(21)=463 (x=461, y=43)
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MAPLE
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isA045636 := proc(n) local p, q ; p := 2 ; while p^2+4 <= n do q := p ; while p^2+q^2 <= n do if q^2+p^2 = n then return true; end if ; q := nextprime(q) ; end do ; p := nextprime(p) ; end do ; return false ; end proc: A066872 := proc(n) ithprime(n)^2+1 ; end: for n from 1 to 200 do if isA045636(A066872(n)) then printf("%d, ", ithprime(n)) ; end if ; end do ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 09 2009]
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CROSSREFS
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Cf. A000040.
Sequence in context: A002733 A108334 A136083 this_sequence A154408 A154411 A089531
Adjacent sequences: A167273 A167274 A167275 this_sequence A167277 A167278 A167279
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 01 2009
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EXTENSIONS
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Edited and extended by Daniel Platt, Nov 02 2009
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