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A001744 Numbers n such that every digit contains a loop (version 2). 24
0, 4, 6, 8, 9, 40, 44, 46, 48, 49, 60, 64, 66, 68, 69, 80, 84, 86, 88, 89, 90, 94, 96, 98, 99, 400, 404, 406, 408, 409, 440, 444, 446, 448, 449, 460, 464, 466, 468, 469, 480, 484, 486, 488, 489, 490, 494, 496, 498, 499, 600, 604, 606, 608, 609, 640, 644, 646 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A001743 for the other version.

If n-1 is represented as a base-5 number (see A007091) according to n-1 = d(m)d(m-1)...d(3)d(2)d(1)d(0) then a(n)= Sum_{j=0..m} c(d(j))*10^j, where c(k)=0,4,6,8,9 for k=0..4. - Hieronymus Fischer, May 30 2012

LINKS

Hieronymus Fischer, Table of n, a(n) for n = 1..10000

Index entries for 10-automatic sequences.

FORMULA

From Hieronymus Fischer, May 30 2012: (Start)

a(n) = ((2*b_m(n)) mod 8 + 4 + floor(b_m(n)/4) - floor((b_m(n)+1)/4))*10^m + sum_{j=0..m-1} ((2*b_j(n))) mod 10 + 2*floor((b_j(n)+4)/5) - floor((b_j(n)+1)/5) -floor(b_j(n)/5)))*10^j, where n>1, b_j(n)) = floor((n-1-5^m)/5^j), m = floor(log_5(n-1)).

a(1*5^n+1) = 4*10^n.

a(2*5^n+1) = 6*10^n.

a(3*5^n+1) = 8*10^n.

a(4*5^n+1) = 9*10^n.

a(n) = 4*10^log_5(n-1) for n=5^k+1,

a(n) < 4*10^log_5(n-1), otherwise.

a(n) > 10^log_5(n-1) n>1.

a(n) = 4*A007091(n-1), iff the digits of A007091(n-1) are 0 or 1.

G.f.: g(x) = (x/(1-x))*sum_{j>=0} 10^j*x^5^j*(1-x^5^j)*(4 + 6x^5^j + 8(x^2)^5^j + 9(x^3)^5^j)/(1-x^5^(j+1)).

Also: g(x) = (x/(1-x))*(4*h_(5,1)(x) + 2*h_(5,2)(x) + 2*h_(5,3)(x) + h_(5,4)(x) - 9*h_(5,5)(x)), where h_(5,k)(x) = sum_{j>=0} 10^j*(x^5^j)^k/(1-(x^5^j)^5). (End)

EXAMPLE

a(1000) = 46999.

a(10^4) = 809999.

a(10^5) = 44499999.

a(10^6) = 668999999.

MATHEMATICA

FromDigits/@Tuples[{0, 4, 6, 8, 9}, 3] (* Harvey P. Dale, Aug 16 2018 *)

PROG

(PARI) is(n) = #setintersect(vecsort(digits(n), , 8), [1, 2, 3, 5, 7])==0 \\ Felix Fröhlich, Sep 09 2019

CROSSREFS

Cf. A061371, A029581, A007091, A046034, A084544, A084984, A017042, A001743, A014261, A014263, A202267, A202268.

Sequence in context: A156673 A073866 A202260 * A113624 A113591 A029581

Adjacent sequences:  A001741 A001742 A001743 * A001745 A001746 A001747

KEYWORD

base,nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Ambiguous comment deleted by Zak Seidov, May 25 2010

Examples added by Hieronymus Fischer, May 30 2012

STATUS

approved

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Last modified October 13 23:52 EDT 2019. Contains 327983 sequences. (Running on oeis4.)