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 A245584 Let f(m) put the leftmost digit of the positive integer m at its end; a(n) is the sequence of all positive integers m with f^2(m)=f(m^2). 1
 1, 2, 3, 12, 122, 1222, 12222, 122222, 1222222, 12222222, 122222222 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA One can easily prove that all integers of the form 12...2 are elements of the sequence. EXAMPLE 122^2=14884 and 221^2=48841. MATHEMATICA f[m_Integer] := Module[{w}, w := IntegerDigits[m]; FromDigits[Rest[AppendTo[w, First[w]]]]]; a245584[n_Integer] := Select[Range[n], If[f[#]^2 == f[#^2] && ! Mod[#, 10] == 0, True, False] &]; a245584[10^5] (* Michael De Vlieger, Aug 17 2014 *) PROG (PYTHON) import math max = 10000 print('los') for n in range(1, max): ...nst = str(n*n) ...nnewst = nst[1:] + nst[0] ...d = int(nnewst) ...e = int(math.sqrt(d)) ...est = str(e) ...enewst = est[len(est)-1] + est[:len(est)-1] ...if (e * e == d) and (nnewst[0] != "0") and (str(n) == enewst): ......print(n, '  ',  e) print('End.') CROSSREFS Cf. A045878, A090843. Sequence in context: A162053 A162075 A333166 * A102878 A132501 A067338 Adjacent sequences:  A245581 A245582 A245583 * A245585 A245586 A245587 KEYWORD nonn,base AUTHOR Reiner Moewald, Jul 26 2014 STATUS approved

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Last modified June 14 17:51 EDT 2021. Contains 345037 sequences. (Running on oeis4.)