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 A272914 Sixth powers ending in digit 6. 8
 4096, 46656, 7529536, 16777216, 191102976, 308915776, 1544804416, 2176782336, 7256313856, 9474296896, 24794911296, 30840979456, 68719476736, 82653950016, 164206490176, 192699928576, 351298031616, 404567235136, 689869781056, 782757789696, 1265319018496, 1418519112256, 2194972623936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Other sequences of k-th powers ending in digit k are: A017281 (k=1), A017355 (k=3), A017333 (k=5), A017311 (k=7), A017385 (k=9). It is missing k=4 because the fourth powers end with 0, 1, 5 or 6. Union of A017322 and A017346. a(h)^(1/6) is a member of A068408 for h = 2, 4, 8, 12, 16, 20, 36, 76, ... LINKS Bruno Berselli, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1). FORMULA O.g.f.: 64*x*(64 + 665*x + 116536*x^2 + 140505*x^3 + 2023280*x^4 + 983830*x^5 + 4720240*x^6 + 983830*x^7 + 2023280*x^8 + 140505*x^9 + 116536*x^10 + 665*x^11 + 64*x^12)/((1 + x)^6*(1 - x)^7). E.g.f.: (-8192 + 45*(91 + 182*x - 5250*x^2 + 16000*x^3 - 9375*x^4 + 1250*x^5)*exp(-x) + (4097 + 287000*x^2 + 1262500*x^3 + 1253125*x^4 + 375000*x^5 + 31250*x^6)*exp(x))/2. a(n) = (10*n - 3*(-1)^n - 5)^6/64 = 64*A047221(n)^6. MATHEMATICA Table[(10 n - 3 (-1)^n - 5)^6/64, {n, 1, 30}] PROG (MAGMA) /* By definition: */ k:=6; [n^k: n in [0..200] | Modexp(n, k, 10) eq k]; (MAGMA) [(10*n-3*(-1)^n-5)^6/64: n in [1..30]]; (PARI) vector(30, n, nn; (10*n-3*(-1)^n-5)^6/64) (Sage) [(10*n-3*(-1)^n-5)^6/64 for n in (1..30)] (Maxima) makelist((10*n-3*(-1)^n-5)^6/64, n, 1, 30); CROSSREFS Cf. A001014, A016746, A017322, A017346 Similar sequences (see comment): A017281, A017311, A017333, A017355, A017385. Sequence in context: A223334 A231945 A220766 * A016996 A218527 A017068 Adjacent sequences:  A272911 A272912 A272913 * A272915 A272916 A272917 KEYWORD nonn,base,easy AUTHOR Bruno Berselli, May 24 2016 STATUS approved

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Last modified December 10 20:55 EST 2018. Contains 318049 sequences. (Running on oeis4.)