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Number of digits in sum of first n primes (A007504).

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1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 (list; graph; listen)

	OFFSET	`1,3`
	COMMENT	`Since A007504(n) has the asymptotic expression ~ n^2 * log(n) / 2, we have a(n) has the asymptotic expression n^2 * log(n) / 2 = floor[log10(10* n^2 * log(n) / 2)] = floor[log10(5* n^2 * log(n))] = floor[log10(5) + log10(n^2) + log10(log(n))] = floor[0.698970004 + 2*log10(n) + log10(log(n))]. What is the smallest n such that a(n) = 5, 6, 7, ...?`
	FORMULA	`a(n) = A055642(A007504(n)) = floor[log10(10*A007504(n))] = A004216(A007504(n))+1 = A004218(A007504(n)+1).`
	EXAMPLE	`a(3) = 2 because 2 + 3 + 5 = 10 has 2 digits in its decimal expansion.`
	MATHEMATICA	`f[n_] := Floor[ Log[10, Sum[Prime@i, {i, n}]] + 1]; Array[f, 105] (* Robert G. Wilson v *)`
	CROSSREFS	`Cf. A000040, A000041, A004216, A004218, A034386, A055642, A111287.` `Sequence in context: A109038 A080342 A081604 this_sequence A099396 A126235 A056556` `Adjacent sequences: A123116 A123117 A123118 this_sequence A123120 A123121 A123122`
	KEYWORD	`base,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 28 2006`
	EXTENSIONS	`More terms from Robert G. Wilson v Oct 05 2006`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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