A247627 Knife numbers (fourth version): n=concat(a,b) is divisible by a+b; a>0 and b may be zero but not have leading zeros.

10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 105, 108, 110, 120, 126, 130, 132, 140, 144, 147, 150, 160, 162, 168, 170, 180, 189, 190, 198, 200, 210, 216, 220, 230, 231, 240, 243, 250, 260, 264, 270, 280, 288, 290, 297, 300, 310, 320, 324, 330, 340, 350, 360, 370, 380, 390, 396, 400

Offset

1,1

Comments

Sequence A247624 is a subsequence, and A247626 contains this as a subsequence, while A247625 is a different variant (with the same inclusion properties).

Links

Table of n, a(n) for n=1..72.

M. F. Hasler in reply to E. Angelini, Re: Knife numbers, SeqFan list, Sep 21 2014.

Example

All n = 10k = concat(k,0) are in this sequence, because k+0 divides n.
However, e.g., 102 is not included since the decomposition in 1+02 is not allowed (and 10+2 does not divide 102).

Prog

(PARI) is(n)=n&&for(k=1, #Str(n)-1, n%([1, 1]*divrem(n, 10^k))==0&&(k==1||n%10^k>=10^(k-1))&&return(1))

Crossrefs

Sequence in context: A158871 A359074 A247626 * A327709 A129120 A134516

Adjacent sequences: A247624 A247625 A247626 * A247628 A247629 A247630

Keyword

nonn,base

Author

M. F. Hasler and Eric Angelini, Sep 21 2014

Status

approved