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 A303068 Numbers k that are multiples of the digital sum of k-1, k and k+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 k == 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 term because it 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 August 18 19:12 EDT 2022. Contains 356215 sequences. (Running on oeis4.)