A346288 Base-10 numbers k such that k has no solutions to k = A * B and R(k) = R(A) * R(B) in any base from base 2 to base 10, and where R(k), the digit reversal of k, is read as a number in the same base.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 19, 20, 21, 23, 25, 29, 31, 32, 35, 37, 40, 41, 43, 47, 53, 55, 59, 60, 61, 65, 67, 70, 71, 73, 75, 77, 79, 80, 83, 85, 87, 89, 92, 94, 97, 98, 100, 101, 103, 106, 107, 109, 113, 114, 115, 127, 128, 129, 131, 137, 139, 141, 142, 145, 147

Offset

1,2

Comments

This sequence uses the same rules to determine the numbers k as A346219 except that here the sequence includes only those numbers which have no solution to the two equalities k = A * B and R(k) = R(A) * R(B) in any base, from base 2 to base 10.

There are 8868747 terms less than 10 million. In that range the longest run where each consecutive number has one or more solutions to the equalities, thus do not appear in this sequence, is from 116 to 126.

Links

Table of n, a(n) for n=1..70.

Example

The first number not in the sequence is 14 as 14 = 2 * 7 and 22 = 2 * 11, and when written in base 5 those become 24 = 2 * 12 and 42 = 2 * 21. These satisfy the two equalities thus 14 is not a term in this sequence.
The second number not in the sequence is 16 as 16 = 2 * 8 and 26 = 2 * 13, which when written in base 6 become 24 = 2 * 12 and 42 = 2 * 21, which satisfy the equalities.
The third number not in the sequence is 18 as 18 = 2 * 9 and 30 = 2 * 15, which when written in base 7 become 24 = 2 * 12 and 42 = 2 * 21, which satisfy the equalities.

Crossrefs

Cf. A346219, A346133, A066531, A230594, A001055, A038548.

Sequence in context: A140401 A272916 A138389 * A032963 A033065 A269445

Adjacent sequences: A346285 A346286 A346287 * A346289 A346290 A346291

Keyword

nonn,base

Author

Scott R. Shannon, Eric Angelini, and Carole Dubois, Jul 12 2021

Status

approved