id:A114216 - OEIS Search Results

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Sum of first n primes divided by maximal power of 2, see formula.

+0
7

1, 1, 3, 5, 1, 7, 3, 11, 17, 23, 27, 1, 21, 1, 3, 7, 33, 47, 57, 1, 37, 29, 7, 3, 25, 63, 83, 95, 51, 41, 21, 19, 39, 89, 119, 135, 73, 59, 113, 143, 161, 171, 181, 187, 3, 101, 39, 131, 179, 51, 71, 155, 99, 175, 27, 145, 207, 239, 129, 205, 61, 177, 121, 27, 85, 201, 133 (list; graph; listen)

	OFFSET	`1,3`
	COMMENT	`a(33899) = 123729 and 33900-th prime is 400559, hence 123729 + 400559 = 524288 = 2^19 and a(33900) = 1. Is a(33900) the last term equal to 1? No other terms with n<10000000. Cf. A114217 values of n for which A114216(n)=1 and A114218 values of k for n with A114216(n)=1.`
	FORMULA	`a(n)=(a(n-1)+n-th prime)/2^k with maximal possible k and with a(1)=1.`
	EXAMPLE	`prime(1)=2 hence a(1)=2/2^2=1; prime(2)=3 hence a(2)=(a(1)+3)/2^2=1; prime(3)=5 hence a(3)=(a(2)+5)/2^1=3; prime(4)=7 hence a(4)=(a(3)+7)/2^1=5 etc.`
	CROSSREFS	`Cf. A114217, A114218.` `Sequence in context: A133045 A158858 A152204 this_sequence A086233 A065395 A112411` `Adjacent sequences: A114213 A114214 A114215 this_sequence A114217 A114218 A114219`
	KEYWORD	`nonn`
	AUTHOR	`Zak Seidov (zakseidov(AT)yahoo.com), Nov 18 2005`

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.

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