A062523 -id:A062523 - cp's OEIS frontend

A100188 Polar structured meta-anti-diamond numbers, the n-th number from a polar structured n-gonal anti-diamond number sequence.

1, 6, 27, 84, 205, 426, 791, 1352, 2169, 3310, 4851, 6876, 9477, 12754, 16815, 21776, 27761, 34902, 43339, 53220, 64701, 77946, 93127, 110424, 130025, 152126, 176931, 204652, 235509, 269730, 307551, 349216

Offset: 1

James A. Record (james.record(AT)gmail.com), Nov 07 2004

			There are no 1- or 2-gonal anti-diamonds, so 1 and (2n+2) are the first and second terms since all the sequences begin as such.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Cf. A000578, A000447, A004466, A007588, A063521, A062523 - "polar" structured anti-diamonds; A100189 - "equatorial" structured meta-anti-diamond numbers; A006484 for other structured meta numbers; and A100145 for more on structured numbers.

[(1/6)*(2*n^4-2*n^2+6*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011

Table[(2n^4-2n^2+6n)/6,{n,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1}, {1,6,27,84,205},40] (* Harvey P. Dale, May 11 2016 *)

vector(40, n, (n^4 -n^2 +3*n)/3) \\ G. C. Greubel, Nov 08 2018

a(n) = (1/6)*(2*n^4 - 2*n^2 + 6*n).
G.f.: x*(1 + x + 7*x^2 - x^3)/(1-x)^5. - Colin Barker, Apr 16 2012
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(1)=1, a(2)=6, a(3)=27, a(4)=84, a(5)=205. - Harvey P. Dale, May 11 2016
E.g.f.: (3*x + 6*x^2 + 6*x^3 + x^4)*exp(x)/3. - G. C. Greubel, Nov 08 2018

A063569 6^a(n) is smallest positive power of 6 containing the string 'n'.

Original entry on oeis.org

9, 3, 3, 2, 6, 6, 1, 5, 12, 4, 9, 16, 4, 13, 28, 18, 3, 10, 15, 21, 26, 3, 22, 12, 27, 26, 17, 7, 16, 4, 13, 22, 24, 12, 27, 19, 2, 21, 22, 30, 13, 14, 22, 25, 17, 15, 6, 15, 28, 15, 21, 31, 46, 23, 28, 18, 6, 15, 20, 17, 10, 8, 11, 33, 14, 6, 6, 8, 18, 9, 11, 22, 26, 17, 16, 33

Offset: 0

Robert G. Wilson v, Aug 10 2001

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Essentially the same as A062523.

a = {}; Do[k = 1; While[ StringPosition[ ToString[6^k], ToString[n] ] == {}, k++ ]; a = Append[a, k], {n, 0, 60} ]; a

def A063569(n):
    m, k, s = 1, 6, str(n)
    while s not in str(k):
        m += 1
        k *= 6
    return m # Chai Wah Wu, Nov 14 2019

A176766 Smallest power of 6 whose decimal expansion contains n.

Original entry on oeis.org

10077696, 1, 216, 36, 46656, 46656, 6, 7776, 2176782336, 1296, 10077696, 2821109907456, 1296, 13060694016, 6140942214464815497216, 101559956668416, 216, 60466176, 470184984576, 21936950640377856, 170581728179578208256, 216

Offset: 0

Jonathan Vos Post, Apr 25 2010

This is to 6 as A176763 is to 3 and as A030001 is to 2.

			a(1) = 1 because 6^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 216 because 6^3 = 216 has "2" as a substring.
a(3) = 36 because 6^2 = 36 has "3" as a substring.

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A000400, A030001, A176763, A176764-A176773.

A176766[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[6^++k], IntegerString[n]]]; 6^k]; Array[A176766, 50, 0] (* Paolo Xausa, Apr 03 2024 *)

a(n) = MIN{A000400(i) such that n in decimal representation is a substring of A000400(i)}.

a(n) = 6^A062523(n). - Michel Marcus, Sep 30 2014

Corrected and extended by Sean A. Irvine and Jon E. Schoenfield, May 05 2010

a(0) prepended by Paolo Xausa, Apr 03 2024

cp's OEIS Frontend

A100188 Polar structured meta-anti-diamond numbers, the n-th number from a polar structured n-gonal anti-diamond number sequence.

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A063569 6^a(n) is smallest positive power of 6 containing the string 'n'.

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A176766 Smallest power of 6 whose decimal expansion contains n.

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