1,1

Leading zeros are not allowed.

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.

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

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

Zak Seidov, Re: 10 different digits, SeqFan list, Jan 03 2012.

234=8+9+67+150

243=8+9+76+150

270=5+8+94+163

306=8+9+75+214

315=7+8+96+204

351=8+9+74+260

360=7+8+94+251

405=8+9+76+312

450=8+9+72+361

459=2+6+81+370

468=2+5+91+370

513=8+9+76+420

531=7+8+96+420

576=2+3+91+480

603=8+9+74+512

612=7+8+94+503

621=8+9+74+530

630=8+9+72+541

702=8+9+54+631

720=5+8+94+613

729=3+5+81+640

738=2+5+91+640

801=6+9+54+732

810=6+9+53+742

819=3+4+62+750

846=2+3+91+750

(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

Sequence in context: A165340 A183985 A184045 * A272767 A104810 A352222

Adjacent sequences: A203600 A203601 A203602 * A203604 A203605 A203606

nonn,base,fini,full

M. F. Hasler and Zak Seidov, Jan 03 2012

Terms > 243 from M. F. Hasler, Jan 03 2012

approved