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A303068 Numbers n that are multiples of the digital sum of n-1, n and n+1. 1
12, 300, 420, 1050, 1200, 1530, 1560, 2100, 2310, 3060, 3432, 5814, 6120, 6240, 9600, 9828, 10200, 10710, 10920, 11100, 11130, 11628, 11700, 12240, 13020, 13260, 16800, 17442, 19656, 20100, 20280, 21210, 21420, 22620, 23256, 23400, 24024, 26010, 29484, 30030 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

n == 0 (mod 6). - Robert G. Wilson v, Apr 28 2018

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..2000

EXAMPLE

12 is a multiple of the sum of digits of 11, 12 and 13: 2, 3 and 4.

MAPLE

s1:=convert(select(n->frac(n/convert(convert(n-1, base, 10), `+`))=0, [$2..31000]), set):

s2:=convert(select(n->frac(n/convert(convert(n, base, 10), `+`))=0, [$2..31000]), set):

s3:=convert(select(n->frac(n/convert(convert(n+1, base, 10), `+`))=0, [$2..31000]), set):

a:=convert(`intersect`(s1, s2, s3), list);

MATHEMATICA

f[n_] := Plus @@ IntegerDigits@n; fQ[n_] := Mod[n, {f[n - 1], f[n], f[n + 1]}] == {0, 0, 0}; Select[ 6 Range@5355, fQ] (* Robert G. Wilson v, Apr 28 2018 *)

PROG

(GAP) a:=Intersection(List([-1, 0, 1], t->List(Filtered(List([2..8000], m->[m, List(List(List([1..m], n->n-t), ListOfDigits), Sum)[m]]), i->i[1] mod i[2]=0), j->j[1])));

(MAGMA) [n: n in [1..31000] | n mod &+Intseq(n+1) eq 0 and n mod &+Intseq(n-1) eq 0 and n mod &+Intseq(n) eq 0]; // Vincenzo Librandi, Apr 29 2018

(PARI) isok(n) = (n>1) && !(n % sumdigits(n-1)) && !(n % sumdigits(n)) && !(n % sumdigits(n+1)); \\ Michel Marcus, Apr 29 2018

CROSSREFS

Intersection of A005349, A160947 and A160948.

Sequence in context: A245915 A109867 A326437 * A014130 A309319 A054942

Adjacent sequences:  A303065 A303066 A303067 * A303069 A303070 A303071

KEYWORD

nonn,base

AUTHOR

Muniru A Asiru, Apr 17 2018

STATUS

approved

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Last modified July 28 23:26 EDT 2021. Contains 346340 sequences. (Running on oeis4.)