A284787 -id:A284787 - cp's OEIS frontend

A284788 Even numbers that cannot be represented in at least two ways as the sum of two odd composites.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 32, 34, 38, 40, 44, 46, 52, 56, 62, 68

Offset: 1

Bernard Schott, Apr 03 2017

If n is even and n > 68, then n can be written as at least two distinct sums of two composite odd integers.

			34 is in the sequence because 34 = 9 + 25 but cannot be represented in a second way as the sum of two odd composites with 9, 15, 21, 25, 27, 33.

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, 1997, page 111.

Cf. A118081, A284787 (complement).

oddco = Select[Range[9, 100, 2], ! PrimeQ[#] &]; Select[Range[2, 100, 2],  Length@ Quiet@ IntegerPartitions[#, {2}, oddco, 2] < 2 &] (* Giovanni Resta, Apr 03 2017 *)

A345339 a(n) = 18*n + 20.

Original entry on oeis.org

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

Offset: 0

Bernard Schott, Jun 14 2021

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).

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

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).

Cf. A076770, A118081, A284787, A284788.

Table[18*n + 20, {n, 0, 55}] (* Amiram Eldar, Jun 14 2021 *)
LinearRecurrence[{2,-1},{20,38},60] (* Harvey P. Dale, Jan 15 2023 *)

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)

cp's OEIS Frontend

A284788 Even numbers that cannot be represented in at least two ways as the sum of two odd composites.

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