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A302801 a(n) is the number whose digits result from the concatenation of the digits of n and the digits of the product of the digits of n.

%I A302801 #20 Mar 10 2024 00:24:28
%S A302801 0,11,22,33,44,55,66,77,88,99,100,111,122,133,144,155,166,177,188,199,
%T A302801 200,212,224,236,248,2510,2612,2714,2816,2918,300,313,326,339,3412,
%U A302801 3515,3618,3721,3824,3927,400,414,428,4312,4416,4520,4624,4728,4832,4936,500,515
%N A302801 a(n) is the number whose digits result from the concatenation of the digits of n and the digits of the product of the digits of n.
%H A302801 Altug Alkan, <a href="/A302801/a302801.png">Line graph of first differences of a(n) for n <= 10^5</a>
%e A302801 For n=10, the digits of n are 1 and 0, their product is 0, and the concatenation gives 1 0 0.
%t A302801 Table[FromDigits[Join[IntegerDigits[n],IntegerDigits[Product[Part[IntegerDigits[n],k],{k,Length[IntegerDigits[n]]}]]]],{n,0,51}] (* _Stefano Spezia_, Aug 13 2023 *)
%o A302801 (PARI) mydigits(n) = if (n, digits(n), [0]);
%o A302801 a(n) = my(d = mydigits(n)); fromdigits(concat(d, mydigits(prod(k=1, #d, d[k]))));
%Y A302801 Cf. A007954, A108773, A302575.
%K A302801 nonn,base,easy
%O A302801 0,2
%A A302801 _Michel Marcus_, Apr 13 2018