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 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 (list; graph; refs; listen; history; text; internal format)
 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:= : 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, 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(#b-1, i, v[b[i+1]+1])); sum(i=1, #d, d[i] * 10^(#d-i)) \\ 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

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Last modified July 12 02:02 EDT 2020. Contains 335658 sequences. (Running on oeis4.)