cp's OEIS Frontend

A380883 a(n) is the smallest multiple of prime(n) which contains every decimal digit of prime(n), including repetitions.

%I A380883 #13 Feb 23 2025 11:24:42
%S A380883 12,30,15,70,110,130,170,190,230,290,310,370,164,344,470,530,295,610,
%T A380883 670,710,730,790,830,890,679,1010,1030,1070,1090,1130,1270,1310,1370,
%U A380883 1390,1490,1510,1570,1630,1670,1730,1790,1810,1719,1930,1379,1990,2110,2230,2270,2290,2330,2390,2410,1255,2570,2367,2690
%N A380883 a(n) is the smallest multiple of prime(n) which contains every decimal digit of prime(n), including repetitions.
%C A380883 Smallest number of the form m*prime(n) such that every decimal digit d in prime(n) (including repetitions) is also a digit in m*prime(n). For every n, m is in {3,4,5,6,7,8,9,10}. The graph displays 8 parallel straight lines, each corresponding to a different value of m (the uppermost being m = 10).
%C A380883 For all n, 10*prime(n) (m = 10) contains all the digits of prime(n), but there are some cases where for m < 10 every digit of prime(n) is found in m*prime(n). The first of these is when n = 1, m = 6; see Example.
%C A380883 This sequence is not the same as A087217(prime(n)) since here the order of digits in m*prime(n)is unimportant; see Example.
%H A380883 Michael De Vlieger, <a href="/A380883/b380883.txt">Table of n, a(n) for n = 1..10000</a>
%H A380883 Michael De Vlieger, <a href="/A380883/a380883.png">Log log scatterplot of a(n)</a>, n = 1..10^5.
%F A380883 a(n) = A380885(prime(n)).
%F A380883 A000040(n) < A380811(n) <= a(n) <= 10*A000040(n).
%e A380883 a(1) = 6*prime(1) = 12.
%e A380883 a(109) = 2995 since prime(109) = 599 and 5*599 = 2995.
%e A380883 For n = 13, prime(13) = 41, a(n) = 164 = 4*31, whereas A097217(41) = 410. This is the first departure from A087217(prime(n)).
%t A380883 Reap[Do[p = Prime[n]; d = DigitCount[p]; k = 2; While[! AllTrue[DigitCount[#] - d, # >= 0 &] &[p*k], k++]; Sow[k *= p], {n, 120}]][[-1, 1]] (* _Michael De Vlieger_, Feb 20 2025 *)
%Y A380883 Cf. A000040, A087217, A380811.
%K A380883 nonn,base
%O A380883 1,1
%A A380883 _David James Sycamore_, Feb 07 2025