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a(n) is the smallest positive number k such that the decimal expansion of n*2^k contains the string n.
2

%I #5 Jan 22 2020 12:57:28

%S 1,4,4,7,4,9,4,8,4,10,10,10,10,10,10,10,10,7,10,10,4,10,10,10,10,10,

%T 10,10,10,10,10,10,10,10,10,10,10,10,10,10,4,10,28,19,13,15,16,40,20,

%U 30,53,27,20,27,35,30,20,53,31,20,4,8,18,35,20,10,30,23,20

%N a(n) is the smallest positive number k such that the decimal expansion of n*2^k contains the string n.

%H Rémy Sigrist, <a href="/A331619/a331619.gp.txt">PARI program for A331619</a>

%e n a(n) n*2^a(n)

%e -- ---- --------

%e 0 1 0

%e 1 4 16

%e 2 4 32

%e 3 7 384

%e 4 4 64

%e 5 9 2560

%e 6 4 96

%e 7 8 1792

%e 8 4 128

%e 9 10 9216

%e 10 10 10240

%Y Cf. A030000, A331440.

%K nonn,base

%O 0,2

%A _Rémy Sigrist_, Jan 22 2020