A078213 Smallest multiple of n beginning and ending in n and with a digit sum that is divisible by n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10810, 119911, 12612, 1310413, 1411214, 15315, 162016, 1745917, 1818, 1968419, 207920, 2116821, 227722, 2318423, 244824, 252925, 269126, 272727, 283528, 2923229, 3069930, 31275931, 3268832, 3375933, 3457834

Offset

1,2

Links

Table of n, a(n) for n=1..34.

Mathematica

smn[n_]:=Module[{k=1, id=IntegerDigits[n], c}, c=k*n; While[Take[ IntegerDigits[ c], IntegerLength[n]]!=id||Take[IntegerDigits[c], -IntegerLength[ n]]!=id||!Divisible[Total[IntegerDigits[k*n]], n], k++; c=k*n]; k*n]; Array[smn, 35] (* Harvey P. Dale, Sep 04 2020 *)

Prog

(PARI) {for(n=1, 34, k=length(Str(n)); s=n; t=s+1; d=k-length(Str(m)); s=s*10^d; t=t*10^d; b=1; while(b>0, q=floor(s/n); while(b>0&&(p=q*n)<t, m=0; z=p; while(z>0, y=divrem(z, 10); z=y[1]; m=m+y[2]); if(p>=s&&(p%10^k) == n&&(m%n) == 0, print1(p, ", "); b=0, q++)); s=10*s; t=10*t))}

Crossrefs

Cf. A078214.

Sequence in context: A082217 A082935 A077739 * A248794 A032555 A032559

Adjacent sequences: A078210 A078211 A078212 * A078214 A078215 A078216

Keyword

base,nonn

Author

Amarnath Murthy, Nov 22 2002

Extensions

Edited and extended by Klaus Brockhaus, Dec 09 2002

Status

approved