id:A063533 - OEIS Search Results

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Hypotenuses of special Pythagorean triples constructed from twin primes as follows: {u, w}={p,p+2}; side a=2p(p+2), side b=(p+2)^2-p^2 and the terms of sequence are values of c=a(n)=p^2+(p+2)^2=Phi[a/2]+1+Sigma[a/2]+1

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34, 74, 290, 650, 1802, 3530, 7202, 10370, 20810, 23330, 38090, 45002, 64802, 73730, 78410, 103970, 115202, 145802, 159050, 194690, 242210, 352802, 373250, 426890, 544970, 649802, 720002, 763850, 824330, 871202, 1312202, 1351370 (list; graph; listen)

	OFFSET	`1,1`
	FORMULA	`a(n) = 2 + A000203[A037074(n)] + A000010[A037074(n)] = A001359[n]^2 + A006512[n]^2`
	EXAMPLE	`a(6) is obtained as follows: u = p = 41, w = p+2 = 43; a = 24143 = 21763 = 3526; b = 432-41^2 = 1849-1681 = 168; c = 43^2+41^2 = 1849+1681 = 3530 = 1+Phi[1763]+1+Sigma[1763] = 1680+1848+2 = a(6); and 3526^2+168^2 = 3530^2.`
	CROSSREFS	`Cf. A001359, A006512, A000010, A000203, A037074, A063530-A063532.` `Sequence in context: A063333 A079863 A154095 this_sequence A118619 A066944 A044172` `Adjacent sequences: A063530 A063531 A063532 this_sequence A063534 A063535 A063536`
	KEYWORD	`nonn`
	AUTHOR	`Labos E. (labos(AT)ana.sote.hu), Aug 02 2001`

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Last modified November 29 12:46 EST 2009. Contains 167659 sequences.

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