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

Offset

0,3

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).

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

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 *)

Prog

(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

Crossrefs

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

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

For primes see A120819.

Sequence in context: A037610 A035239 A344183 * A252043 A014824 A060555

Adjacent sequences: A057134 A057135 A057136 * A057138 A057139 A057140

Keyword

base,easy,nonn

Author

Henry Bottomley, Aug 12 2000

Status

approved