A203603 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.

153, 162, 180, 189, 207, 216, 234, 243, 270, 306, 315, 351, 360, 405, 450, 459, 468, 513, 531, 576, 603, 612, 621, 630, 702, 720, 729, 738, 801, 810, 819, 846

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..32.

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

Example

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

Prog

(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

Crossrefs

Sequence in context: A165340 A183985 A184045 * A272767 A104810 A352222

Adjacent sequences: A203600 A203601 A203602 * A203604 A203605 A203606

Keyword

nonn,base,fini,full

Author

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

Extensions

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

Status

approved