A034115 Fractional part of square root of a(n) starts with 9: first term of runs.

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

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

a(n) ~ n^2. - Charles R Greathouse IV, May 29 2026

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 *)

Prog

(PARI) a(n)=(5*n^2+49*n+[125, 121, 122, 123, 124][n%5+1])/5 \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. A027690, A034105, A090223, A034115.

Sequence in context: A110264 A389221 A034105 * A212600 A247135 A391328

Adjacent sequences: A034112 A034113 A034114 * A034116 A034117 A034118

Keyword

nonn,base,easy,changed

Author

Patrick De Geest, Sep 15 1998

Status

approved