A057137 Concatenate next digit at right hand end (where the next digit after 9 is again 0).

0, 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 1234567890, 12345678901, 123456789012, 1234567890123, 12345678901234, 123456789012345, 1234567890123456, 12345678901234567, 123456789012345678, 1234567890123456789, 12345678901234567890, 123456789012345678901

Offset: 0

Author

Henry Bottomley, Aug 12 2000

Keywords

• base
• easy
• nonn

Comments

Also called the triangle of the gods (see Pickover link).

See A037610 for a general formula. - Hieronymus Fischer, Jan 03 2013

References

• Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61.

Links

• T. D. Noe and Hieronymus Fischer, Table of n, a(n) for n = 0..200 (terms up to 100 from T. D. Noe)
• Clifford Pickover, Triangle of the Gods
• Index entries for linear recurrences with constant coefficients, signature (10,0,0,0,0,0,0,0,0,1,-10).

Crossrefs

Alternative progression for n >= 10 compared with A007908 and A014824.

Cf. A057138 for reverse. Cf. A010879 (decimal digits).

For primes see A120819.

Programs

Maple

A057137:=n->floor((137174210/1111111111)*10^n); seq(A057137(n), n=0..20); # Wesley Ivan Hurt, Apr 18 2014

Mathematica

a[n_]:=Floor[137174210/1111111111*10^n]; Array[a,19,0] (* Robert G. Wilson v, Apr 18 2014 *)

PARI

A057137(n)=sum(i=1,n,i%10*10^(n-i)) \\ M. F. Hasler, Jan 13 2013

PARI

A057137(n)=137174210*10^n\1111111111 \\ M. F. Hasler, Jan 13 2013

Python

def A057137(n): s = '0123456789'; return int((n+1)//10*s + s[:(n+1)%10]) # Ya-Ping Lu, Apr 08 2025

Formula

a(n) = 10*(a(n-1)-floor[n/10]) + n = floor[A057139(n)/10^(n-1)].

a(n) = floor((137174210/1111111111)*10^n). - Hieronymus Fischer, Jan 03 2013, corrected by M. F. Hasler, Jan 13 2013