A276037 Numbers using only digits 1 and 5.

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

Offset: 1

Author

Vincenzo Librandi, Aug 17 2016

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

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

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).

Programs

Magma

[n: n in [1..20000] | Set(Intseq(n)) subset {1, 5}]; // Vincenzo Librandi, Aug 19 2016

Maple

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

Mathematica

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

PARI

a(n) = my(v=[1,5], b=binary(n+1), d=vector(#b-1,i, v[b[i+1]+1])); sum(i=1, #d, d[i] * 10^(#d-i)) \\ David A. Corneth, Aug 22 2016

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

Python

def A276037(n): return (int(bin(n+1)[3:])<<2)+(10**((n+1).bit_length()-1)-1)//9 # Chai Wah Wu, Jun 28 2025

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)

Extensions

Example changed by David A. Corneth, Aug 22 2016