A345339 - OEIS

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A345339

a(n) = 18*n + 20.

20, 38, 56, 74, 92, 110, 128, 146, 164, 182, 200, 218, 236, 254, 272, 290, 308, 326, 344, 362, 380, 398, 416, 434, 452, 470, 488, 506, 524, 542, 560, 578, 596, 614, 632, 650, 668, 686, 704, 722, 740, 758, 776, 794, 812, 830, 848, 866, 884, 902, 920, 938, 956, 974, 992, 1010

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OFFSET

0,1

COMMENTS

The largest even integer which cannot be written as the sum of 2n composite odd integers, for n >= 1, is 18*n + 20, proved by the Shippensburg University Mathematical Problem Solving Group (see Links).

LINKS

Table of n, a(n) for n=0..55.

Ronald E. Ruemmler, Problem 1328, Mathematics Magazine, Vol. 62, No. 4 (October 1989), p. 274; Sums of Composite Odd Numbers, Solution to problem 1328 by Garrett R. Vargas, ibid., Vol. 63, No. 4 (October 1990), pp. 276-277.

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

FORMULA

a(n) = 18*n + 20.

G.f.: 2*(10 - x)/(1 - x)^2. - Stefano Spezia, Jun 14 2021

From Elmo R. Oliveira, Dec 08 2024: (Start)

E.g.f.: 2*exp(x)*(10 + 9*x).

a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

EXAMPLE

For n = 1, a(1) = A118081(14) = 38.

MATHEMATICA

Table[18*n + 20, {n, 0, 55}] (* Amiram Eldar, Jun 14 2021 *)

LinearRecurrence[{2, -1}, {20, 38}, 60] (* Harvey P. Dale, Jan 15 2023 *)