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

Author

Scott R. Shannon, Apr 28 2024

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

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