A266281 a(1)=1; a(n) is the first integer > a(n-1) with which, in the a(n-1)/a(n) decimal expansion, n is present.

1, 4, 11, 13, 14, 17, 19, 22, 23, 29, 34, 47, 58, 61, 65, 87, 89, 93, 94, 97, 102, 103, 105, 109, 113, 115, 116, 118, 121, 130, 131, 136, 139, 141, 149, 152, 157, 159, 161, 166, 167, 169, 174, 177, 179, 181, 184, 188, 191, 193, 194, 197, 199, 203, 218, 223, 224

Offset

1,2

Comments

Two other sequences are possible without the a(n)>a(n-1) limitation, one with a(n) terms already used in the sequences (where the n growth does not allow data looping), another only with a(n) terms not yet used.

Links

Francesco Di Matteo, Table of n, a(n) for n = 1..1000

Example

a(8) = 22 because a(7) = 19 and "8" does not appear in the digital expansion of 19/20 = 0.95 nor of 19/21 = 0.904761904761..., but it does appear in 19/22 = 0.86363...;
a(9) = 23 because 22/23 = 0.9565217391304..., where "9" does appear;
a(10) = 29 because "10" does not appear in the digital expansion of 23/k for k=24..28, but it does appear in 23/29 = 0.7931034...

Mathematica

f[n_] := Block[{a = {1}, k}, Do[k = a[[m - 1]] + 1; While[SequenceCount[Flatten@ First@ RealDigits[a[[m - 1]]/k], IntegerDigits@ m] < 1, k++]; AppendTo[a, k], {m, 2, n}]; a]; f@ 57 (* Version 10.1, or *)
f[n_] := Block[{a = {1}, k}, Do[k = a[[m - 1]] + 1; While[StringCount[
ToString[FromDigits@ Flatten@ First@ RealDigits[a[[m - 1]]/k]], ToString@ m] < 1, k++]; AppendTo[a, k], {m, 2, n}]; a]; f@ 57 (* Michael De Vlieger, Dec 30 2015, Version 5.1 *)

Prog

(Python)
alfa = 1
for n in range(2, 101):
    beta = alfa
    aflag = 0
    while aflag == 0:
        beta = beta + 1
        restlist = []
        result = ""
        dividend = alfa
        lenn = len(str(n))
        bflag = 0
        while bflag < lenn:
            dividend = dividend * 10
            q = dividend/beta
            resto = dividend - (q * beta)
            if resto == 0:
                bflag = lenn
            if resto in restlist:
                bflag = bflag + 1
            restlist.append(resto)
            dividend = resto
            result = result + str(q)
            if str(n) in result:
                bflag = lenn
                aflag = 1
    print alfa
    alfa = beta

Crossrefs

Cf. A257664, A265740, A265756.

Sequence in context: A098060 A268232 A285633 * A154040 A066985 A228003

Adjacent sequences: A266278 A266279 A266280 * A266282 A266283 A266284

Keyword

nonn,base

Author

Francesco Di Matteo, Dec 26 2015

Status

approved