A203603 - OEIS

%I #20 Dec 23 2024 14:53:43

%S 153,162,180,189,207,216,234,243,270,306,315,351,360,405,450,459,468,

%T 513,531,576,603,612,621,630,702,720,729,738,801,810,819,846

%N Numbers n=a+b+c+d such that 0<a<b<c<d and concatenation(n,a,b,c,d) is a permutation of the digits 0,...,9.

%C Leading zeros are not allowed.

%C Only 3-digit numbers are possible under the given constraints: If n had only 2 digits, then n <= 98 and a+b+c+d >= 10+25+36+47 > 100. If n had 4 digits, then n >= 1023 and a+b+c+d <= 4+5+6+987 < 1015.

%C The summands a,b,c,d can have length 1,1,2,3 or 1,2,2,2.

%C The idea and terms < 270 are from M. Levin, cf. link.

%H Zak Seidov, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2012-January/008831.html">Re: 10 different digits</a>, SeqFan list, Jan 03 2012.

%e 234=8+9+67+150

%e 243=8+9+76+150

%e 270=5+8+94+163

%e 306=8+9+75+214

%e 315=7+8+96+204

%e 351=8+9+74+260

%e 360=7+8+94+251

%e 405=8+9+76+312

%e 450=8+9+72+361

%e 459=2+6+81+370

%e 468=2+5+91+370

%e 513=8+9+76+420

%e 531=7+8+96+420

%e 576=2+3+91+480

%e 603=8+9+74+512

%e 612=7+8+94+503

%e 621=8+9+74+530

%e 630=8+9+72+541

%e 702=8+9+54+631

%e 720=5+8+94+613

%e 729=3+5+81+640

%e 738=2+5+91+640

%e 801=6+9+54+732

%e 810=6+9+53+742

%e 819=3+4+62+750

%e 846=2+3+91+750

%o (PARI) is_A203603(n)={ my( t, d=eval( setminus( Vec("0123456789"), vecsort( Vec( Str( n )),,8))), v1=[1,1,10,1,1,10,100]~, v2=[1,10,10,1,1,1,10]~); n<999 & #d==7 & for( p=1,7!, t=vecextract(d,numtoperm(7,p)); n != t*v1 & n != t*v2 & next; t[1] * t[2] * t[3] * t[7] & return( if( n == t*v1, Str( t[2]"+"t[1]"+"t[3],t[4]"+"t[7],t[6],t[5] ),t )))}  \\ _M. F. Hasler_, Jan 03 2012

%K nonn,base,fini,full

%O 1,1

%A _M. F. Hasler_ and _Zak Seidov_, Jan 03 2012

%E Terms > 243 from _M. F. Hasler_, Jan 03 2012