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a(n) is the smallest positive integer not yet appearing in the sequence such that n*a(n) contains n as a substring.
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%I #40 Feb 08 2024 10:44:47

%S 1,6,10,11,3,16,21,23,22,31,100,26,87,51,41,73,69,66,63,36,58,101,97,

%T 52,5,102,103,46,79,61,107,76,192,151,81,38,201,89,164,35,59,34,173,

%U 126,99,184,74,135,153,7,167,176,29,251,121,28,168,148,27,56,92,123,137,57,141,207,25,113

%N a(n) is the smallest positive integer not yet appearing in the sequence such that n*a(n) contains n as a substring.

%H Scott R. Shannon, <a href="/A333410/b333410.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A333410/a333410.gp.txt">PARI program for A333410</a>

%e a(2) = 6 as 6 has not appeared previously and 2 * 6 = 12 which contains '2' as a substring.

%e a(6) = 16 as 16 has not appeared previously and 6 * 16 = 96 which contains '6' as a substring.

%e a(7) = 21 as 21 has not appeared previously and 7 * 21 = 147 which contains '7' as a substring.

%o (PARI) See Links section.

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o s, mink, aset, concat = 1, 2, {1}, "1"

%o yield from [1]

%o for n in count(2):

%o an, sn = mink, str(n)

%o while an in aset or not sn in str(n*an): an += 1

%o aset.add(an); s += an; concat += str(an); yield an

%o while mink in aset: mink += 1

%o print(list(islice(agen(), 68))) # _Michael S. Branicky_, Feb 08 2024

%Y Cf. A086064, A333774, A333775, A333811, A332795, A332703.

%K nonn,base

%O 1,2

%A _Scott R. Shannon_, Apr 11 2020