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 A306853 Positive integers equal to the permanent of the circulant matrix formed by their decimal digits. 1
 1, 2, 3, 4, 5, 6, 7, 8, 9, 261, 370, 407, 52036, 724212 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 1, 2, 3, 4, 5, 6, 7, 8, 9, 370 and 407 are also equal to the determinant of the circulant matrix formed by their decimal digits. LINKS Eric Weisstein's World of Mathematics, Permanent Eric Weisstein's World of Mathematics, Circulant Matrix EXAMPLE | 2 6 1 | perm | 1 2 6 | = 2*2*2 + 6*6*6 + 1*1*1 + 1*2*6 + 6*1*2 + 2*6*1 = 261.      | 6 1 2 | MAPLE with(linalg): P:=proc(q) local a, b, c, d, i, j, k, n, t; for n from 1 to q do d:=ilog10(n)+1; a:=convert(n, base, 10); c:=[]; for k from 1 to nops(a) do c:=[op(c), a[-k]]; od; t:=[op([]), c]; for k from 2 to d do b:=[op([]), c[nops(c)]]; for j from 1 to nops(c)-1 do b:=[op(b), c[j]]; od; c:=b; t:=[op(t), c]; od; if n=permanent(t) then print(n); fi; od; end: P(10^7); PROG (PARI) mpd(n) = {my(d = digits(n)); matpermanent(matrix(#d, #d, i, j, d[1+lift(Mod(j-i, #d))])); } isok(n) = mpd(n) == n; \\ Michel Marcus, Mar 14 2019 CROSSREFS Cf. A219324, A219327, A306662, A306593, A306714. Up to n=110 the permanent of the circulant matrix of the digits of n is equal to A101337 but from n=111 on it can differ. Sequence in context: A085134 A229761 A004882 * A308110 A306593 A046469 Adjacent sequences:  A306850 A306851 A306852 * A306854 A306855 A306856 KEYWORD nonn,base,more AUTHOR Paolo P. Lava, Mar 13 2019 STATUS approved

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Last modified June 6 11:08 EDT 2020. Contains 334829 sequences. (Running on oeis4.)