A372336 For a positive number k, let L(k) denote the list consisting of k followed by the prime factors of k, with repetition, in nondecreasing order; sequence gives composite k such that the digits of L(k) alternate being smaller than and then larger than the previous digit.

6, 51, 91, 106, 219, 323, 406, 435, 437, 518, 529, 609, 614, 626, 629, 634, 658, 703, 705, 818, 826, 838, 878, 906, 938, 978, 2051, 2093, 2173, 3053, 3241, 4151, 4171, 4281, 5041, 5063, 5141, 5183, 5241, 6251, 6591, 7021, 7081, 7251, 8051, 8121, 8491, 8571, 8781, 9121, 9231, 9291, 9583

Offset

1,1

Comments

No term can end in 0 or 2; a number ending in 2 would mean the first prime factor is 2, which would disqualify the number, while a number ending in 0 would mean the first 3 distinct prime factors would have to be 2, 3, 5 or 2, 5, either of which would also disqualify the number.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Example

106 is a term as 106 = 2 * 53 which when concatenated give "106253", the digits of which alternate from being smaller than and then larger than the previous digit.

Crossrefs

Cf. A372335, A372280, A372308, A372034, A372029, A056704.

Sequence in context: A292818 A173082 A113653 * A133395 A341424 A372731

Adjacent sequences: A372333 A372334 A372335 * A372337 A372338 A372339

Keyword

nonn,base

Author

Scott R. Shannon, Apr 28 2024

Status

approved