A337733 - OEIS

%I #28 Sep 25 2020 10:27:35

%S 4,16,24,56,81,88,138,144,192,242,250,297,366,408,456,516,520,522,564,

%T 575,704,744,777,795,819,884,900,912,966,1008,1053,1071,1080,1104,

%U 1134,1250,1312,1316,1375,1512,1520,1608,1644,1680,1712,1778,1928,1950,2025,2048,2072

%N 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.

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

%C 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?

%H <a href="/index/Coi#Colombian">Index to sequences related to Colombian numbers</a>.

%e 4 = 2 + 2 = 2 + 2 = 2 * 2;

%e 16 = 8 + 8 = 8 + 8 = 4 * 4;

%e 24 = 21 + (2+1) = 17 + (1*7) = 12 * (1*2);

%e 56 = 46 + (4+6) = 51 + (5*1) = 14 * (1*4);

%e 81 = 72 + (7+2) = 63 + (6*3) = 9 * 9.

%t 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 *)

%o (PARI) isok(m) = {if (m==0, return (1)); for (k=1, m,  if (k+vecprod(digits(k)) == m, return (1)); ); } \\ A337718

%o listb(nn) = Vec(setintersect(Set(vector(nn, k, k+sumdigits(k))), Set(vector(nn, k, k*vecprod(digits(k)))))); \\ A336983

%o lista(nn) = select(x->isok(x), listb(nn)); \\ _Michel Marcus_, Sep 18 2020

%Y Intersection of A176995, A336826 and A337718.

%Y Intersection of A336983 and A337718.

%Y Cf. A004023, A337139.

%K nonn,base

%O 1,1

%A _Bernard Schott_, Sep 18 2020

%E More terms from _Michel Marcus_, Sep 18 2020