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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.
1
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?
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.
Sequence in context: A145229 A174999 A160996 * A173926 A305884 A239522
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Sep 18 2020
EXTENSIONS
More terms from Michel Marcus, Sep 18 2020
STATUS
approved