

A276037


Numbers using only digits 1 and 5.


16



1, 5, 11, 15, 51, 55, 111, 115, 151, 155, 511, 515, 551, 555, 1111, 1115, 1151, 1155, 1511, 1515, 1551, 1555, 5111, 5115, 5151, 5155, 5511, 5515, 5551, 5555, 11111, 11115, 11151, 11155, 11511, 11515, 11551, 11555, 15111, 15115, 15151, 15155, 15511, 15515
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OFFSET

1,2


COMMENTS

Numbers n such that product of digits of n is a power of 5.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..8190


FORMULA

From Robert Israel, Aug 22 2016: (Start)
a(2n+1) = 10 a(n) + 1.
a(2n+2) = 10 a(n) + 5.
G.f. g(x) satisfies g(x) = 10 (x + x^2) g(x^2) + (x + 5 x^2)/(1  x^2). (End)


EXAMPLE

5551 is in the sequence because all of its digits are 1 or 5 and consequently because the product of digits, 5*5*5*1 = 125 = 5^3 is a power of 5.


MAPLE

S[0]:= [0]:
for d from 1 to 6 do S[d]:= map(t > (10*t+1, 10*t+5), S[d1]) od:
seq(op(S[d]), d=1..6); # Robert Israel, Aug 22 2016


MATHEMATICA

Select[Range[20000], IntegerQ[Log[5, Times@@(IntegerDigits[#])]]&]


PROG

(Python)
from itertools import product
A276037_list = [int(''.join(d)) for l in range(1, 10) for d in product('15', repeat=l)] # Chai Wah Wu, Aug 18 2016
(MAGMA) [n: n in [1..20000]  Set(Intseq(n)) subset {1, 5}]; // Vincenzo Librandi, Aug 19 2016
(PARI) a(n) = my(v=[1, 5], b=binary(n+1), d=vector(#b1, i, v[b[i+1]+1])); sum(i=1, #d, d[i] * 10^(#di)) \\ David A. Corneth, Aug 22 2016


CROSSREFS

Cf. numbers n such that product of digits of n is a power of k: A028846 (k=2), A174813 (k=3), this sequence (k=5), A276038 (k=6), A276039 (k=7).
Cf. A199985 (a subsequence).
Sequence in context: A136976 A136975 A136973 * A221743 A137008 A137010
Adjacent sequences: A276034 A276035 A276036 * A276038 A276039 A276040


KEYWORD

nonn,base


AUTHOR

Vincenzo Librandi, Aug 17 2016


EXTENSIONS

Example changed by David A. Corneth, Aug 22 2016


STATUS

approved



