A169967 -id:A169967 - cp's OEIS frontend

A078243 Smallest multiple of n using only digits 0 and 4.

4, 4, 444, 4, 40, 444, 4004, 40, 444444444, 40, 44, 444, 4004, 4004, 4440, 400, 44404, 444444444, 44004, 40, 40404, 44, 440404, 4440, 400, 4004, 4404444444, 4004, 4404404, 4440, 444044, 4000, 444444, 44404, 40040, 444444444, 444, 44004, 40404

Offset: 1

Amarnath Murthy, Nov 23 2002

a(n) = min{A169967(k): k > 1 and A169967(k) mod n = 0}. [Reinhard Zumkeller, Jan 10 2012]

Reinhard Zumkeller, Table of n, a(n) for n = 1..998

Cf. A004290, A078241-A078248, A079339, A096681-A096688.

a078243 n = head [x | x <- tail a169967_list, mod x n == 0]
-- Reinhard Zumkeller, Jan 10 2012

More terms from Ray Chandler, Jul 12 2004

A268620 Numbers whose digital sum is a multiple of 4.

Original entry on oeis.org

0, 4, 8, 13, 17, 22, 26, 31, 35, 39, 40, 44, 48, 53, 57, 62, 66, 71, 75, 79, 80, 84, 88, 93, 97, 103, 107, 112, 116, 121, 125, 129, 130, 134, 138, 143, 147, 152, 156, 161, 165, 169, 170, 174, 178, 183, 187, 192, 196, 202, 206, 211, 215, 219, 220, 224, 228, 233, 237, 242, 246

Offset: 1

Bruno Berselli, Feb 09 2016

a(1498) = 5999 is the smallest term that is congruent to 5 modulo 9.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007953, A061383 (supersequence).
Cf. numbers whose digital sum is a multiple of k: A054683 (k=2), A008585 (k=3), this sequence (k=4), A227793 (k=5).
Subsequences: A002278, A038446, A052218, A052222, A061387, A169967, A235151, A235227, A235229.

[n: n in [0..250] | IsIntegral(&+Intseq(n)/4)];

select(t -> convert(convert(t,base,10),`+`) mod 4 = 0, [$1..1000]); # Robert Israel, Feb 09 2016

Select[Range[0, 250], IntegerQ[Total[IntegerDigits[#]]/4] &]

A284972 Numbers with digits 4 and 8 only.

Original entry on oeis.org

4, 8, 44, 48, 84, 88, 444, 448, 484, 488, 844, 848, 884, 888, 4444, 4448, 4484, 4488, 4844, 4848, 4884, 4888, 8444, 8448, 8484, 8488, 8844, 8848, 8884, 8888, 44444, 44448, 44484, 44488, 44844, 44848, 44884, 44888, 48444, 48448, 48484, 48488, 48844, 48848

Offset: 1

Jaroslav Krizek, Apr 07 2017

All terms are even.

Numbers with digits 4 and k only for k = 0 - 3 and 5 - 9: A169967 (k = 0), A032822 (k = 1), A284920 (k = 2), A032834 (k = 3), A256290 (k = 5), A284634 (k = 6), A284971 (k = 7), this sequence (k = 8), A284973 (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {4, 8}]

Flatten@ Table[FromDigits /@ Tuples[{4, 8}, n], {n, 5}] (* Giovanni Resta, Apr 07 2017 *)

a(n) = my (b = binary(1+n)); b[1] = 0; return (4*(10^(#b-1)-1)/(10-1) + (8-4)*fromdigits(b)) \\ Rémy Sigrist, Apr 08 2017

a(n)={my(v=binary(n+1));v[1]=0;v+=vector(#v,i,i>1);4*fromdigits(v)} \\ R. J. Cano, Apr 08 2017

a(n,{p=[4,8]})={my(v=binary(n+1));fromdigits(vector(#v-1,i,p[2]*v[i+1]+p[1]*!v[i+1]))} \\ R. J. Cano, Apr 09 2017

a(n) = 2 * A284920(n) = 4 * A032822(n).

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A078243 Smallest multiple of n using only digits 0 and 4.

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A268620 Numbers whose digital sum is a multiple of 4.

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A284972 Numbers with digits 4 and 8 only.

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