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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.
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%I #8 Apr 28 2024 09:35:11

%S 6,51,91,106,219,323,406,435,437,518,529,609,614,626,629,634,658,703,

%T 705,818,826,838,878,906,938,978,2051,2093,2173,3053,3241,4151,4171,

%U 4281,5041,5063,5141,5183,5241,6251,6591,7021,7081,7251,8051,8121,8491,8571,8781,9121,9231,9291,9583

%N 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.

%C 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.

%H Scott R. Shannon, <a href="/A372336/b372336.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

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

%K nonn,base

%O 1,1

%A _Scott R. Shannon_, Apr 28 2024