This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380811 #18 Feb 05 2025 22:14:04
%S A380811 12,30,15,70,110,39,51,95,92,203,93,74,123,301,94,159,295,122,268,142,
%T A380811 365,237,332,178,194,202,206,214,218,339,254,393,274,417,298,453,314,
%U A380811 326,501,346,537,1086,955,386,394,398,422,892,1362,916,932,956,482,502,514
%N A380811 Smallest composite number divisible by prime(n) which shares at least one decimal digit with prime(n).
%C A380811 10*prime(n) contains all the digits of prime(n), but is not always the smallest such number.
%H A380811 Michael De Vlieger, <a href="/A380811/b380811.txt">Table of n, a(n) for n = 1..10000</a>
%H A380811 Michael De Vlieger, <a href="/A380811/a380811.png">Log log scatterplot of a(n)</a>, n = 1..10^6.
%F A380811 a(n) <= 10*prime(n), with equality when n = 2,4,5.... (doubtful if there are any more)
%e A380811 123 is the smallest number divisible by prime(13) = 41 which shares at least one decimal digit (1) of 41, so a(13) = 123.
%e A380811 218 is the smallest number divisible by prime(29) = 109 which shares at least one decimal digit (1) with 109, so a(29) = 218.
%t A380811 Table[p = Prime[n]; d = IntegerDigits[p]; m = 1; Until[k = m*p; IntersectingQ[d, IntegerDigits[k]], m++]; k, {n, 120}] (* _Michael De Vlieger_, Feb 05 2025 *)
%o A380811 (PARI) a(n) = my(p = prime(n), d = Set(digits(p))); for(i = 2, oo, if(#setintersect(d, Set(digits(i*p))) > 0, return(i*p))) \\ _David A. Corneth_, Feb 05 2025
%Y A380811 Cf. A000040.
%K A380811 nonn,base
%O A380811 1,1
%A A380811 _David James Sycamore_, Feb 04 2025
%E A380811 More terms from _David A. Corneth_, Feb 05 2025