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A034115 Fractional part of square root of a(n) starts with 9: first term of runs. 2
35, 48, 63, 80, 99, 119, 142, 167, 194, 223, 253, 286, 321, 358, 397, 437, 480, 525, 572, 621, 671, 724, 779, 836, 895, 955, 1018, 1083, 1150, 1219, 1289, 1362, 1437, 1514, 1593, 1673, 1756, 1841, 1928, 2017, 2107, 2200, 2295, 2392, 2491, 2591, 2694 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

How is this different from A034105? - N. J. A. Sloane, Mar 30 2007

Answer: A034115 has the starts of runs of consecutive values of A034105.  That is, frac{sqrt[a(n)]} >= 0.9, but frac{sqrt[a(n)-1]} < 0.9. - Don Reble, Jul 17 2020

LINKS

Table of n, a(n) for n=1..47.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

FORMULA

a(n) = n^2 + 9*n + 25 + floor(4*n / 5) = A027690(n+4)+A090223(n). - Don Reble, Jul 17 2020

EXAMPLE

358, 359 and 360 are a run of 3 numbers in A034105, so 358 is in this sequence, but 359 and 360 are not. - R. J. Mathar, Jul 21 2020

MATHEMATICA

Join[{35}, Select[Partition[Select[Range[3000], NumberDigit[Sqrt[#], -1] == 9&], 2, 1], (#[[2]]-#[[1]]!=1&)][[All, 2]]] (* or *) LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {35, 48, 63, 80, 99, 119, 142}, 50] (* Harvey P. Dale, Aug 14 2021 *)

CROSSREFS

Cf. A027690, A034105, A090223.

Sequence in context: A033857 A110264 A034105 * A212600 A247135 A249819

Adjacent sequences:  A034112 A034113 A034114 * A034116 A034117 A034118

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Sep 15 1998

STATUS

approved

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Last modified October 4 18:13 EDT 2022. Contains 357239 sequences. (Running on oeis4.)