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

68, 39, 19, 18, 23, 22, 14, 17, 14, 12, 11, 13, 11, 13, 12, 13, 11, 14, 10, 15, 14, 13, 9, 11, 13, 9, 15, 14, 13, 12, 11, 15, 10, 7, 12, 9, 12, 10, 11, 8, 11, 8, 12, 11, 13, 13, 10, 12, 10, 8, 11, 12, 9, 7, 6, 7, 8, 12, 8, 8, 7, 7, 10, 9, 9, 6, 9, 10, 9, 10

Offset

1,1

Comments

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.

References

E.I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig-Jena-Berlin, 2. Auflage 1982.

Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

2^68 = 295147905179352825856 (21 digits), 3^39 = 4052555153018976267 (19)
5^19 = 19073486328125 (14), 7^18 = 1628413597910449 (16), 11^23 = 895430243255237372246531 (24)
13^22 = 3211838877954855105157369 (25), 17^14 = 168377826559400929 (18)
19^17 = 5480386857784802185939 (22), 23^14 = 11592836324538749809 (20)
29^12 = 353814783205469041 (18), 31^11 = 25408476896404831 (17)
37^13 = 243569224216081305397 (21), 41^11 = 550329031716248441 (18)
43^13 = 1718264124282290785243 (22), 47^12 = 116191483108948578241 (21)
53^13 = 26036721925606486195973 (23), 59^11 = 30155888444737842659 (20)
61^14 = 9876832533361318095112441 (25), 67^10 = 1822837804551761449 (19)
71^15 = 5873205959385493353867330551 (28), 73^14 = 122045014039746588673695409 (23)
79^13 = 4668229371502258117133839 (25), 83^9 = 186940255267540403 (18)
89^11 = 2775173073766990340489 (22), 97^13 = 67302709016557486028618977 (26)
101^9 = 1093685272684360901 (19), 103^15 = 1557967416600764580522382952407 (31)
107^14 = 25785341502012466393542552649 (29), 109^13 = 306580461214335498944273629 (27)
113^12 = 4334523100191686738306881 (25), 127^11 = 138624799340320978519423 (24)

Mathematica

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 *)

Prog

(PARI) a(n) = {my(k=1, p=prime(n)); while(#Set(digits(p^k))<10, k++); k; } \\ Jinyuan Wang, Aug 14 2020

Crossrefs

Cf. A049363, A050278, A050288, A171132.

Sequence in context: A033388 A196109 A196106 * A090493 A259081 A143737

Adjacent sequences: A171741 A171742 A171743 * A171745 A171746 A171747

Keyword

nonn,base

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 17 2009

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

Corrected and extended by Harvey P. Dale, Aug 03 2019

Status

approved