A057934 - OEIS

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A057934

Number of prime factors of 10^n + 1 (counted with multiplicity).

1, 1, 3, 2, 2, 2, 2, 2, 5, 3, 5, 3, 3, 4, 7, 5, 4, 3, 2, 4, 8, 4, 5, 3, 5, 3, 7, 4, 3, 7, 2, 4, 9, 4, 5, 6, 4, 3, 10, 4, 3, 7, 4, 4, 12, 4, 4, 9, 4, 7, 8, 4, 2, 6, 10, 5, 6, 5, 4, 6, 3, 3, 12, 3, 6, 8, 2, 4, 10, 11, 3, 5, 4, 7, 11, 6, 12, 7, 4, 9, 11, 3, 7, 8, 8, 3, 8, 4, 4, 11, 6, 4, 8, 4, 6, 8, 4, 5, 13 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,3`
	COMMENTS	`2^(a(2n)-1)-1 predicts the number of pair_solutions of even length L for AB = A^2 + B^2. For instance with length 18 we have 10^18 + 1 = 101.9901.999999000001 or 3 divisors F which when put into the Mersenne formula 2^(F-1)-1 yields 3 pairs (see reference 'Puzzle 104' for details).`
	LINKS	`C. Rivera, Puzzle 104` `S. S. Wagstaff, Jr., Main Tables from the Cunningham Project.` `S. S. Wagstaff, Jr., The Cunningham Project`
	FORMULA	`a(n) = A057951(2n) - A057951(n) - T. D. Noe (noe(AT)sspectra.com), Jun 19 2003`
	CROSSREFS	`Cf. A003021, A001271, A046053, A057935-A057941, A054992, A001562.` `Cf. A057951.` `Sequence in context: A058758 A104223 A119704 * A122396 A037199 A145376` `Adjacent sequences: A057931 A057932 A057933 * A057935 A057936 A057937`
	KEYWORD	`nonn`
	AUTHOR	`Patrick De Geest (pdg(AT)worldofnumbers.com), Oct 15 2000.`

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Last modified February 17 11:16 EST 2012. Contains 206011 sequences.