A230099 -id:A230099 - cp's OEIS frontend

A243218 Number of n-digit integers x such that x + A007954(x) has n digits, where A007954(x) is the product of decimal digits of x.

5, 63, 756, 8268, 86225, 880519, 8898517, 89471520, 897248572, 8985712192, 89925825853, 899614672173, 8997997446679, 89989593213308, 899945924502919, 8999718992342921, 89998539650321017, 899992410699128981, 8999960560129165187, 89999795045731606967

Offset: 1

Michel Marcus, Jun 01 2014

			For n=1, the five 1-digit integers 0,1,2,3,4 satisfy the condition, with results being respectively 0,2,4,6 and 8, hence a(1)=5.

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..35

Cf. A007954, A230099, A242945, A243219.

DP(n)= my(d = digits(n)); prod(i=1, #d, d[i]);
a(n) = {nb = 0; if (n==1, istart = 0, istart = 10^(n-1)); for (i=istart, 10^n-1, if (i + DP(i) < 10^n, nb++);); nb;}

a(9)-a(17) from Hiroaki Yamanouchi, Sep 29 2014

a(18)-a(20) from Hiroaki Yamanouchi, Jan 08 2016

A337732 Least positive number that has exactly n different representations as the sum of a number and the product of its decimal digits.

Original entry on oeis.org

1, 0, 10, 50, 150, 1014, 9450, 8305, 283055, 931395, 92441055, 84305555, 28322235955

Offset: 0

Bernard Schott, Sep 18 2020

Least integer m such that A230103(m) = n.

			10 = 5 + 5 = 10 + 1*0 and as 10 is the smallest number with 2 such representations, so, a(2) = 10.
50 = 35 + 3*5 = 42 * 4*2 = 50 + 5*0 and as 50 is the smallest number with 3 such representations, so, a(3) = 50.

Cf. A230099, A230103, A337718.

Cf. A337051 (similar for Bogotá numbers).

f[n_] := n + Times @@ IntegerDigits[n]; m = 10^6; v = Table[0, {m}]; Do[i = f[n] + 1; If[i <= m, v[[i]]++], {n, 0, m}]; s = {1}; k = 1; While[(p = Position[v, k]) != {}, AppendTo[s, p[[1, 1]] - 1]; k++]; s (* Amiram Eldar, Sep 18 2020 *)

f(n) = if (n==0, return(1)); sum(k=1, n, k+vecprod(digits(k)) == n); \\ A230103
a(n) = my(k=0); while(f(k) !=n, k++); k; \\ Michel Marcus, Sep 18 2020

a(4)-a(7) from Michel Marcus, Sep 18 2020
a(8)-a(11) from Amiram Eldar, Sep 18 2020
a(12) from Bert Dobbelaere, Sep 22 2020

A337843 a(n) is n + the number of digits in the decimal expansion of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69

Offset: 0

Jaroslav Krizek, Sep 25 2020

a(n) is an increasing injective sequence that is not surjective.
a(n) is also the sequence of numbers m that can be written as (m + number of digits of m) for some m >= 0, complement of numbers from A081552(n) for n > 1.
Sequence is not the same as A101947, first different term is a(77) = 79.

			a(10) = 10 + 2 = 12.

Cf. A055642, A062028, A081552, A230099.

Cf. A110803 (n * the number of digits in the decimal expansion of n).

[1] cat [n + #Intseq(n): n in [1..100]];

a[0] = 1; a[n_] := n + IntegerLength[n]; Array[a, 100, 0] (* Amiram Eldar, Sep 25 2020 *)

a(n) = if (n==0, 1, n + #digits(n)); \\ Michel Marcus, Sep 26 2020

a(n) = n + A055642(n).

cp's OEIS Frontend

A243218 Number of n-digit integers x such that x + A007954(x) has n digits, where A007954(x) is the product of decimal digits of x.

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A337732 Least positive number that has exactly n different representations as the sum of a number and the product of its decimal digits.

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A337843 a(n) is n + the number of digits in the decimal expansion of n.

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