A323422 Multiples of three whose sum of digits is not divisible by 3 until the final digit.

0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 42, 45, 48, 51, 54, 57, 72, 75, 78, 81, 84, 87, 102, 105, 108, 111, 114, 117, 132, 135, 138, 141, 144, 147, 162, 165, 168, 171, 174, 177, 192, 195, 198, 201, 204, 207, 222, 225, 228, 231, 234, 237, 252, 255, 258, 261, 264, 267, 282, 285, 288, 291, 294, 297

Offset

1,2

Comments

An integer is a member if, when its digits are added from left to right, the sum is divisible by 3 only when all the digits have been added.

If m is in the sequence then so is m1 = m + 3*10^k and m1 and m have the same number of digits such that the addition gives no carries. For example, 12 is in the sequence so is 12 + 30 = 42 as there is no carry and 12 and 42 have the same number of digits.

Links

Cyril Naud, Table of n, a(n) for n = 1..9999

Example

117 is a term because the consecutive sums are 1, 2(=1+1), 9(=1+1+7) : only the last sum is divisible by 3.
123 is not a term because 1+2 is divisible by 3.

Prog

(JavaScript)
var i=0, sequence=[];
while(true)
{
var i_str=i.toString();
var digits=[];
for(var j=0; j<is.length; j++)
digits.push(parseInt(i_str.charAt(j)));
var sum=0, ok=true;
for(var k=0; k<digits.length; k++)
{
sum+=digits[k];
if((sum%n==0&&k<digits.length-1)||(sum%n!=0&&k==digits.length-1))
  ok=false
}
if(ok)
sequence.push(i);
  i++;
}
(PARI) is(n) = if(n / 3 != n \ 3, return(0)); my(d = digits(n), s = 0); for(i = 1, #d - 1, s += d[i]; if(s % 3 == 0, return(0))); 1 \\ David A. Corneth, Jan 14 2019

Crossrefs

Subsequence of A008585.

Sequence in context: A085126 A190083 A117124 * A071073 A329844 A127451

Adjacent sequences: A323419 A323420 A323421 * A323423 A323424 A323425

Keyword

nonn,base,easy

Author

Cyril Naud, Jan 14 2019

Status

approved