A363909 - OEIS

%I #9 Aug 02 2023 14:02:04

%S 6534,11027,11994,21906,22178,22195,23317,24567,27019,27963,28354,

%T 29099,29309,29339,29375,29558,29621,30184,30552,30584,31578,31727,

%U 32447,32633,32793,32912,32923,33087,33257,33527,34284,35717,36943,36958,37697,38463

%N Numbers whose square and cube taken together contain each decimal digit at least twice.

%C The first term, a(1) = 6534 is the only number of which the square and cube taken together contain each digit 0 to 9 exactly twice.

%C Presumably a(n) ~ A363905(n) ~ n. - _Charles R Greathouse IV_, Jul 03 2023

%H Harold Suarez, <a href="https://www.linkedin.com/feed/update/urn:li:activity:7073402002042417152">Interesting...</a>, Number Theory group on LinkedIn, (<a href="https://media.licdn.com/dms/image/D4E22AQGcSX5-sppg5w/feedshare-shrink_480/0/1686422952129?e=1691020800&amp;v=beta&amp;t=meKHAYtIqdAZAqXfIrwv8pNchJHW7lAayXEcDZf9dU0">capture of the original post</a>), June 2023

%e 6534^2 = 42693156, 6534^3 = 278957081304, which together contain each digit 0-9 exactly twice.

%o (PARI) is(n)=#Set(n=concat(digits(n^2),digits(n^3)))>9&&(n=vecsort(n))[#n-1]==9&&!n[2]&&!for(i=3,#n-2,n[i]>n[i-1]&&n[i]<n[i+1]&&return)

%o select(is,[2111..39999])

%Y Cf. A363905: square and cube together contain each digit at least once.

%Y Cf. A036744, A054038, A071519 and A156977 for "pandigital" squares.

%Y Cf. A119735: Numbers n such that every digit occurs at least once in n^3.

%K nonn,base,less

%O 1,1

%A _M. F. Hasler_, Jun 27 2023