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A057137 Concatenate next digit at right hand end (where the next digit after 9 is again 0). 10
0, 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 1234567890, 12345678901, 123456789012, 1234567890123, 12345678901234, 123456789012345, 1234567890123456, 12345678901234567, 123456789012345678 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

For primes see A120819.

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

Index of terms which are prime: 171, 277, 367, 561, 567, 18881, ..., (A120819). - Robert G. Wilson v, Apr 18 2014

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

FORMULA

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

a(n) = 10*a(n-1) + (n mod 10). - Paolo P. Lava, Feb 01 2008

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.

See also A120819.

Sequence in context: A037701 A037610 A035239 * A252043 A014824 A060555

Adjacent sequences:  A057134 A057135 A057136 * A057138 A057139 A057140

KEYWORD

base,easy,nonn

AUTHOR

Henry Bottomley, Aug 12 2000

STATUS

approved

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Last modified May 28 21:38 EDT 2017. Contains 287241 sequences.