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 A030288 a(n+1) is smallest square > a(n) having no digits in common with a(n), with a(0) = 0. 3
 0, 1, 4, 9, 16, 25, 36, 49, 81, 225, 361, 400, 529, 676, 841, 900, 1156, 2209, 3136, 4225, 6889, 7225, 8100, 24336, 58081, 69696, 70225, 84681, 90000, 111556, 200704, 316969, 407044, 511225, 608400, 923521, 4000000, 5112121, 6036849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 LINKS David W. Wilson and Jon E. Schoenfield, Table of n, a(n) for n = 0..250 (first 231 terms from David W. Wilson) FORMULA a(n) = A030287(n)^2. - Michel Marcus, Nov 03 2017 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A000290, A019544, A030098, A030287, A030289. Sequence in context: A179126 A068879 A030152 * A030154 A122541 A133743 Adjacent sequences:  A030285 A030286 A030287 * A030289 A030290 A030291 KEYWORD nonn,base AUTHOR STATUS approved

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Last modified October 23 23:21 EDT 2019. Contains 328379 sequences. (Running on oeis4.)