A143031 A sequence of asymptotic density zeta(5) - 1, where zeta is the Riemann zeta function.

15, 47, 79, 111, 143, 158, 175, 207, 239, 271, 303, 320, 335, 367, 399, 431, 463, 495, 527, 559, 591, 623, 644, 655, 687, 719, 751, 783, 806, 815, 847, 879, 911, 943, 975, 1007, 1039, 1071, 1103, 1130, 1135, 1167, 1199, 1231, 1263, 1292, 1295, 1327, 1359

Offset

1,1

Comments

Made up of a collection of mutually exclusive residue classes modulo multiples of factorials. A set of such sequences with entries for each zeta(k) - 1 partitions the integers. See the linked paper for their construction.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

William J. Keith, Sequences of Density zeta(K) - 1, INTEGERS, Vol. 10 (2010), Article #A19, pp. 233-241. Also arXiv preprint, arXiv:0905.3765 [math.NT], 2009 and author's copy.

Mathematica

f[n_] := Module[{k = n - 1, m = 2, r}, While[{k, r} = QuotientRemainder[k, m]; r != 0, m++]; IntegerExponent[k + 1, m] + 2]; Select[Range[1400], f[#] == 5 &] (* Amiram Eldar, Feb 15 2021 after Kevin Ryde at A161189 *)

Crossrefs

Cf. A143028, A143029, A143030, A143032, A143033, A143034, A143035, A143036, A161189, A339013.

Sequence in context: A045111 A031451 A105572 * A214675 A166118 A063396

Adjacent sequences: A143028 A143029 A143030 * A143032 A143033 A143034

Keyword

nonn

Author

William J. Keith, Jul 18 2008

Status

approved