1,3

Base-10 representation Sum_{i=0..m} d(i)*10^i has d(m) >= d(m-1) >=... >= d(1) >= d(0).

These numbers might be called "Nialpdromes".

A004186(a(n)) = a(n). -Reinhard Zumkeller,Oct 31 2007

Reinhard Zumkeller,Table of n, a(n) for n = 1..1000

D. Applegate, M. LeBrun, and N. J. A. Sloane,Dismal Arithmetic,J. Int. Seq. 14 (2011) # 11.9.8.

David A. Corneth,Table of n, a(n) for n = 1..20000,Jun 03 2014

Eric Weisstein's World of Mathematics,Digit

Binomial(n+k,k) = (n+k)!/(n!*k!). d(i) is the i-th digit of a(n). q is the number of digits of a(n). Find the highest m such that C(10 + m, 10) - m + 1 <= n. a(n) has m+1 digits. Set n = n - C(10+m,10). Find the highest d(m+1), then d(m), then..., then d(1) each iteration such that C(d(m+1)+m+1,1+m+1)<=n. Then set n = n-C(d(m+1)+m+1,m+2). If n = 0 then stop. All remaining digits are 0.

As 10000 = C(10+6,10) - 6 + C(7+6,1+6) + C(5+5,1+5) + C(4+4,1+4) + C(3+3,1+3) + C(1+2,1+2) + C(0+1,1+1), C(0+0,1+0), a(10000) = 7543100.

Select[Range[0, 211], GreaterEqual@@IntegerDigits[#]&] (*Ray Chandler,Oct 25 2011 *)

(PARI) is(n)=my(d=digits(n)); for(i=2, #d, if(d[i]>d[i-1], return(0))); 1 \\Charles R Greathouse IV,Jan 02 2014

(PARI) \\ This program is optimized for fast calculation of a(n) for large n.

a(n)={my(q, m=10, i, r=0); n--; while(binomial(m+1, 10)<=n+m-9, m++); n-=binomial(m, 10); n+=m-9; q=m-9; i=q; while(n>0, m=i; while(binomial(m+1, i)<=n, m++); r=10*r+m+1-i; n-=binomial(m, i); i--; ); z=q-#digits(r); r*=10^z; r} \\David A. Corneth,Jun 01 2014

(PARI) \\recursive--feed an element a(n)>0 and it gives a(n+1).

nxt(n)={my(r, d=digits(n), y, t); if(d[#d]!=9, y=1; while(y-#d-1&&d[y]==9, y++); t=#d; forstep(i=t, y+1, -1, if(d[i-1]!=d[i], t=i-1; break)); if(t!=#d, d[t+1]++; for(i=t+2, #d, d[i]=0), d[y]++; for(i=y+1, #d, d[i]=0)); r=d, d=vector(#d+1); d[1]=1; for(i=2, #d, d[i]=0); r=d); sum(i=1, #r, 10^(#r-i)*r[i])} \\David A. Corneth,Jun 01 2014

(Python)

from itertools import count, islice, combinations_with_replacement as mc

def agen(): # generator of terms

yield 0

for d in count(1):

ni = (int( "".join(m)) for m in mc( "9876543210", d) if m[0]!= "0" )

yield from sorted(ni)

print(list(islice(agen(), 70))) #Michael S. Branicky,Jun 24 2022

Differs fromA032873andA032907.

Cf.A064222,A152054.

Sequence in context:A084383A032873A072543*A032907A130576A334145

Adjacent sequences:A009993A009994A009995*A009997A009998A009999

nonn,base,look

Corrected byRick L. Shepherd,Jun 06 2002

approved