A337733 Numbers that can be written as (k + sum of digits of k) for some k, also as (m + product of digits of m) for some m, and finally as (q * product of digits of q) for some q.

4, 16, 24, 56, 81, 88, 138, 144, 192, 242, 250, 297, 366, 408, 456, 516, 520, 522, 564, 575, 704, 744, 777, 795, 819, 884, 900, 912, 966, 1008, 1053, 1071, 1080, 1104, 1134, 1250, 1312, 1316, 1375, 1512, 1520, 1608, 1644, 1680, 1712, 1778, 1928, 1950, 2025, 2048, 2072

Offset

1,1

Comments

Equivalently, Bogotá numbers that are not Colombian and that can be written as (m + product of digits of m) for some m.

The only primes that can belong to this sequence are repunits > 11 whose indices are in A004023. It is known that these primes belong to A336983, but do they belong also to A337718?

Links

Table of n, a(n) for n=1..51.

Index to sequences related to Colombian numbers.

Example

4 = 2 + 2 = 2 + 2 = 2 * 2;
16 = 8 + 8 = 8 + 8 = 4 * 4;
24 = 21 + (2+1) = 17 + (1*7) = 12 * (1*2);
56 = 46 + (4+6) = 51 + (5*1) = 14 * (1*4);
81 = 72 + (7+2) = 63 + (6*3) = 9 * 9.

Mathematica

m = 2100; Select[Intersection @@ Union /@ Transpose[Table[{n + Plus @@ (d = IntegerDigits[n]), n + (p = Times @@ d), n*p}, {n, 1, m}]], # <= m &] (* Amiram Eldar, Sep 18 2020 *)

Prog

(PARI) isok(m) = {if (m==0, return (1)); for (k=1, m,  if (k+vecprod(digits(k)) == m, return (1)); ); } \\ A337718
listb(nn) = Vec(setintersect(Set(vector(nn, k, k+sumdigits(k))), Set(vector(nn, k, k*vecprod(digits(k)))))); \\ A336983
lista(nn) = select(x->isok(x), listb(nn)); \\ Michel Marcus, Sep 18 2020

Crossrefs

Intersection of A176995, A336826 and A337718.

Intersection of A336983 and A337718.

Cf. A004023, A337139.

Sequence in context: A145229 A174999 A160996 * A173926 A305884 A239522

Adjacent sequences: A337730 A337731 A337732 * A337734 A337735 A337736

Keyword

nonn,base

Author

Bernard Schott, Sep 18 2020

Extensions

More terms from Michel Marcus, Sep 18 2020

Status

approved