A063533 - OEIS

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A063533

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.

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; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Table of n, a(n) for n=1..32.`
	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: A154095 A184066 A277449 * A216432 A118619 A258413` `Adjacent sequences: A063530 A063531 A063532 * A063534 A063535 A063536`
	KEYWORD	`nonn`
	AUTHOR	`Labos Elemer, Aug 02 2001`
	STATUS	`approved`

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Last modified December 2 19:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)