A087599 Smallest nonzero n-digit term of A087597, or 0 if no such number exists.

1, 10, 105, 2211, 16836, 105111, 2220778, 14319276, 221098906, 1087061878, 11402689605, 223577504556, 1264725045100, 50869724563503, 111335989114503, 2399795843858155, 11141229266441550, 127955437456464996, 1070124037258522456

Offset: 1

Author

Amarnath Murthy, Sep 18 2003

Keywords

• base
• nonn

Comments

Conjecture: No term is zero.

Examples

			a(4) = 2211, A040115(2211) = 10.
		

Crossrefs

Cf. A000217, A040115, A087597, A087598, A087600.

Programs

PARI

dd(k)={ local(kshf,res,dig,odig,p) ; kshf=k ; res=0 ; odig=kshf % 10 ; p=0 ; while(kshf>9, kshf=floor(kshf/10) ; dig=kshf % 10 ; res += 10^p*abs(dig-odig) ; odig=dig ; p++ ; ) ; return(res) ; } isA000217(n)={ if( issquare(1+8*n), return(1), return(0) ) ; } A000217(n)={ return(n*(n+1)/2) ; } ndigs(n)={ local(nshft,res) ; res=0 ; nshft=n; while(nshft>0, res++ ; nshft=floor(nshft/10) ; ) ; return(res) ; } isA087597(n)={ if( isA000217(n) && isA000217(dd(n)), return(1), return(0) ) ; } A087599(n)={ local(k,T) ; k=floor(-0.5+sqrt(0.25+2*10^(n-1))) ; T=A000217(k) ; if(ndigs(T)A000217(k) ; if(ndigs(T)>n, return(0) ) ; if( isA087597(T), return(T) ) ; k++ ; ) ; } { for(n=2,21, print1(A087599(n),",") ; ) ; } \\ R. J. Mathar, Nov 19 2006

Extensions

Corrected and extended by R. J. Mathar, Nov 19 2006

a(14)-a(18) from Donovan Johnson, May 08 2010

a(19) from Donovan Johnson, Jun 19 2011

a(1)=1 prepended by Max Alekseyev, Jul 27 2024