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 A355660 Numbers m such that the smallest number of pentagonal numbers (A000326) which sum to m is exactly 4. 2
 4, 8, 16, 19, 20, 26, 30, 33, 38, 42, 50, 54, 60, 65, 67, 77, 81, 84, 88, 90, 96, 99, 100, 101, 111, 112, 113, 120, 125, 131, 135, 138, 142, 154, 159, 160, 166, 170, 171, 183, 195, 204, 205, 207, 217, 224, 225, 226, 229, 230, 236, 240, 241, 243, 255, 265, 275, 277, 286, 306, 308, 345 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Richard Blecksmith & John Selfridge found 204 such integers among the first million, the largest of which is 33066. They believe that they have found them all (Richard K. Guy reference). a(205) > 10^11, if it exists, from Giovanni Resta in A003679. REFERENCES Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section D3, Figurate numbers, pp. 222-228. LINKS Table of n, a(n) for n=1..62. Richard K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172. FORMULA A100878(a(n)) = 4. EXAMPLE 4 = 1 + 1 + 1 + 1. 8 = 5 + 1 + 1 + 1. 16 = 5 + 5 + 5 + 1. Also, it is not possible to get these terms when summing three or fewer pentagonal numbers. MATHEMATICA nn = 100; pen = Table[n (3n - 1)/2, {n, 0, nn - 1}]; lst = Range[pen[[-1]]]; Do[n = pen[[i]]+pen[[j]]+pen[[k]]; If[n <= pen[[-1]], lst = DeleteCases[lst, n]], {i, 1, nn}, {j, i, nn}, {k, j, nn}]; A003679 = lst; Complement[A003679, {9, 21, 31, 43, 55, 89}] (* Jean-François Alcover, Jul 13 2022, after T. D. Noe in A003679 *) CROSSREFS Cf. A000326, A100878. Equals A003679 \ A133929. Sequence in context: A181310 A212110 A033310 * A312785 A312786 A312787 Adjacent sequences: A355657 A355658 A355659 * A355661 A355662 A355663 KEYWORD nonn AUTHOR Bernard Schott, Jul 12 2022 STATUS approved

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Last modified May 29 17:30 EDT 2023. Contains 363042 sequences. (Running on oeis4.)