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

%I A057137 #65 Apr 08 2025 21:55:21
%S A057137 0,1,12,123,1234,12345,123456,1234567,12345678,123456789,1234567890,
%T A057137 12345678901,123456789012,1234567890123,12345678901234,
%U A057137 123456789012345,1234567890123456,12345678901234567,123456789012345678,1234567890123456789,12345678901234567890,123456789012345678901
%N A057137 Concatenate next digit at right hand end (where the next digit after 9 is again 0).
%C A057137 Also called the triangle of the gods (see Pickover link).
%C A057137 See A037610 for a general formula. - _Hieronymus Fischer_, Jan 03 2013
%D A057137 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61.
%H A057137 T. D. Noe and Hieronymus Fischer, <a href="/A057137/b057137.txt">Table of n, a(n) for n = 0..200</a> (terms up to 100 from T. D. Noe)
%H A057137 Clifford Pickover, <a href="http://sprott.physics.wisc.edu/Pickover/trianglegod.htm">Triangle of the Gods</a>
%H A057137 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (10,0,0,0,0,0,0,0,0,1,-10).
%F A057137 a(n) = 10*(a(n-1)-floor[n/10]) + n = floor[A057139(n)/10^(n-1)].
%F A057137 a(n) = floor((137174210/1111111111)*10^n). - _Hieronymus Fischer_, Jan 03 2013, corrected by _M. F. Hasler_, Jan 13 2013
%p A057137 A057137:=n->floor((137174210/1111111111)*10^n); seq(A057137(n), n=0..20); # _Wesley Ivan Hurt_, Apr 18 2014
%t A057137 a[n_]:=Floor[137174210/1111111111*10^n]; Array[a,19,0] (* _Robert G. Wilson v_, Apr 18 2014 *)
%o A057137 (PARI) A057137(n)=sum(i=1,n,i%10*10^(n-i)) \\ _M. F. Hasler_, Jan 13 2013
%o A057137 (PARI) A057137(n)=137174210*10^n\1111111111 \\ _M. F. Hasler_, Jan 13 2013
%o A057137 (Python) def A057137(n): s = '0123456789'; return int((n+1)//10*s + s[:(n+1)%10]) # _Ya-Ping Lu_, Apr 08 2025
%Y A057137 Alternative progression for n >= 10 compared with A007908 and A014824.
%Y A057137 Cf. A057138 for reverse. Cf. A010879 (decimal digits).
%Y A057137 For primes see A120819.
%K A057137 base,easy,nonn
%O A057137 0,3
%A A057137 _Henry Bottomley_, Aug 12 2000