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URL: https://oeis.org/A323422

⇱ A323422 - OEIS

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A323422
Multiples of three whose sum of digits is not divisible by 3 until the final digit.
1
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.
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
KEYWORD
nonn,base,easy
AUTHOR
Cyril Naud, Jan 14 2019
STATUS
approved