A341354 - OEIS

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A341354

Greatest k such that 3^k divides A156552(2*n); number of trailing 1-digits in the ternary expansion of A156552(n).

0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 3, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 3, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 0, 0, 0, 4, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 4, 0, 0 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,5`
	COMMENTS	`The 3-adic valuation of A156552(2*n).`
	LINKS	`Antti Karttunen, Table of n, a(n) for n = 1..65539` `Index entries for sequences computed from indices in prime factorization`
	FORMULA	`a(n) = A341353(2n) = A007949(A156552(2n)) = A007949(1+(2A156552(n))).` `For all n >= 1, a(A000040(2n)) = a(n^2) = 0.`
	PROG	`(PARI)` `A007949(n) = valuation(n, 3);` `A156552(n) = { my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };` `A341354(n) = A007949(A156552(2*n));`
	CROSSREFS	`Even bisection of A341353.` `Cf. A000040, A007949, A156552, A341355.` `Cf. A329604 (positions of nonzero terms).` `Sequence in context: A057918 A242192 A016380 * A203945 A212663 A341774` `Adjacent sequences: A341351 A341352 A341353 * A341355 A341356 A341357`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Feb 14 2021`
	STATUS	`approved`

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Last modified June 2 09:14 EDT 2024. Contains 373033 sequences. (Running on oeis4.)