A373444 Positive integers that cannot be written as a sum of a practical number and a heptagonal number.

10, 14, 44, 45, 51, 53, 68, 69, 77, 86, 92, 110, 125, 131, 170, 173, 179, 182, 206, 233, 266, 284, 296, 303, 373, 377, 383, 425, 437, 444, 479, 524, 536, 584, 719, 845, 1124, 1133, 1208, 1325, 1358, 1445, 1478, 1499, 1562, 1626, 1787, 1947, 1979, 2117, 2249, 2252, 2273, 2747, 2957, 3209, 3341, 4058, 4268, 5609, 6830, 8006, 8333, 9284, 11699, 12164, 14024, 17432, 21257, 24797, 25919, 33773, 79445

Offset

1,1

Comments

Somu and Tran (2024) conjectured that there are finitely many such integers. It was also conjectured that 79445 is the largest such integer. This conjecture was checked up to 10^8.

Links

Table of n, a(n) for n=1..73.

Sai Teja Somu and Duc Van Khanh Tran, On sums of practical numbers and polygonal numbers, Journal of Integer Sequences, 27(5), 2024.

Crossrefs

Cf. A000566, A005153.

Sequence in context: A328635 A260564 A107126 * A371618 A247091 A025122

Adjacent sequences: A373441 A373442 A373443 * A373445 A373446 A373447

Keyword

nonn,hard

Author

Duc Van Khanh Tran, Jun 05 2024

Status

approved