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A171744 a(n) is the smallest exponent such that prime(n)^k is pandigital in base 10.

%I A171744 #19 Oct 12 2024 01:53:31
%S A171744 68,39,19,18,23,22,14,17,14,12,11,13,11,13,12,13,11,14,10,15,14,13,9,
%T A171744 11,13,9,15,14,13,12,11,15,10,7,12,9,12,10,11,8,11,8,12,11,13,13,10,
%U A171744 12,10,8,11,12,9,7,6,7,8,12,8,8,7,7,10,9,9,6,9,10,9,10
%N A171744 a(n) is the smallest exponent such that prime(n)^k is pandigital in base 10.
%C A171744 A pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once.
%D A171744 E.I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig-Jena-Berlin, 2. Auflage 1982.
%D A171744 Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983.
%H A171744 David A. Corneth, <a href="/A171744/b171744.txt">Table of n, a(n) for n = 1..10000</a>
%e A171744 2^68 = 295147905179352825856 (21 digits), 3^39 = 4052555153018976267 (19)
%e A171744 5^19 = 19073486328125 (14), 7^18 = 1628413597910449 (16), 11^23 = 895430243255237372246531 (24)
%e A171744 13^22 = 3211838877954855105157369 (25), 17^14 = 168377826559400929 (18)
%e A171744 19^17 = 5480386857784802185939 (22), 23^14 = 11592836324538749809 (20)
%e A171744 29^12 = 353814783205469041 (18), 31^11 = 25408476896404831 (17)
%e A171744 37^13 = 243569224216081305397 (21), 41^11 = 550329031716248441 (18)
%e A171744 43^13 = 1718264124282290785243 (22), 47^12 = 116191483108948578241 (21)
%e A171744 53^13 = 26036721925606486195973 (23), 59^11 = 30155888444737842659 (20)
%e A171744 61^14 = 9876832533361318095112441 (25), 67^10 = 1822837804551761449 (19)
%e A171744 71^15 = 5873205959385493353867330551 (28), 73^14 = 122045014039746588673695409 (23)
%e A171744 79^13 = 4668229371502258117133839 (25), 83^9 = 186940255267540403 (18)
%e A171744 89^11 = 2775173073766990340489 (22), 97^13 = 67302709016557486028618977 (26)
%e A171744 101^9 = 1093685272684360901 (19), 103^15 = 1557967416600764580522382952407 (31)
%e A171744 107^14 = 25785341502012466393542552649 (29), 109^13 = 306580461214335498944273629 (27)
%e A171744 113^12 = 4334523100191686738306881 (25), 127^11 = 138624799340320978519423 (24)
%t A171744 sepan[n_]:=Module[{p=Prime[n],k=1},While[Min[DigitCount[p^k]]==0,k++];k]; Array[sepan,100] (* _Harvey P. Dale_, Aug 03 2019 *)
%o A171744 (PARI) a(n) = {my(k=1, p=prime(n)); while(#Set(digits(p^k))<10, k++); k; } \\ _Jinyuan Wang_, Aug 14 2020
%Y A171744 Cf. A049363, A050278, A050288, A171132.
%K A171744 nonn,base
%O A171744 1,1
%A A171744 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 17 2009
%E A171744 Edited by _Charles R Greathouse IV_, Aug 02 2010
%E A171744 Corrected and extended by _Harvey P. Dale_, Aug 03 2019