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

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

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

Examples

			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
		

Links

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

Crossrefs

Cf. A027690, A034105, A090223.

Programs

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 *)

Formula

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