A030288 - OEIS

%I #31 Sep 10 2024 19:55:20

%S 0,1,4,9,16,25,36,49,81,225,361,400,529,676,841,900,1156,2209,3136,

%T 4225,6889,7225,8100,24336,58081,69696,70225,84681,90000,111556,

%U 200704,316969,407044,511225,608400,923521,4000000,5112121,6036849

%N a(n+1) is smallest square > a(n) having no digits in common with a(n), with a(0) = 0.

%C It appears that from a(102) on, there is a 4-periodic pattern: a(4k) ~ 3*10^(k-3) a(4k+1) ~ 6.1111...*10^(k-3), a(4k+2) ~ 7*10^(k-3), a(4k+3) ~ 8.1111...*10^(k-3), where ~ means the next larger square which has only digits {0, 3, 4, 5, 7} for even-indexed terms, or {1, 2, 6, 8, 9} for odd-indexed terms. - _M. F. Hasler_, Nov 12 2017

%H David W. Wilson and Jon E. Schoenfield, <a href="/A030288/b030288.txt">Table of n, a(n) for n = 0..250 (first 231 terms from David W. Wilson)</a>

%F a(n) = A030287(n)^2. - _Michel Marcus_, Nov 03 2017

%t FromDigits /@ NestList[Block[{k = Sqrt@ FromDigits@ # + 1, m}, While[ContainsAny[#, Set[m, IntegerDigits[k^2]]], k++]; m] &, {0}, 38] (* _Michael De Vlieger_, Nov 02 2017 *)

%t ssga[a_]:=Module[{k=Floor[Sqrt[a]]+1},While[Length[Intersection[IntegerDigits[k^2],IntegerDigits[ a]]]> 0,k++];k^2]; NestList[ssga,0,40] (* _Harvey P. Dale_, Sep 10 2024 *)

%o (PARI) next_A030288(n, D(n)=Set(digits(n)), S=D(n))={for(k=sqrtint(n)+1, oo, #setintersect(D(k^2), S)||return(k^2))} \\ Could be made more efficient by implementing the observed patterns, in particular for n >= 104. - _M. F. Hasler_, Nov 12 2017

%Y Cf. A000290, A019544, A030098, A030287, A030289.

%K nonn,base

%O 0,3

%A _Patrick De Geest_