A047892 -id:A047892 - cp's OEIS frontend

A047903 a(1) = 13; for n > 0, a(n+1) = a(n) * sum of digits of a(n).

13, 52, 364, 4732, 75712, 1665664, 56632576, 2265303040, 56632576000, 2265303040000, 56632576000000, 2265303040000000, 56632576000000000, 2265303040000000000, 56632576000000000000, 2265303040000000000000

Offset: 1

Miklos SZABO (mike(AT)ludens.elte.hu)

After the 7th element, every second element has the same beginning. a(9+2k) = 40 * a(8+2k) = 40 * 25 * a(7+2k).

Cf. A047892.

NestList[# Total[IntegerDigits[#]]&,13,20] (* Harvey P. Dale, Jan 08 2019 *)

A140131 a(n) = a(n-1) + a(n-2) + digsum(a(n-1)) + digsum(a(n-2)), with a(0)=0 and a(1)=1.

Original entry on oeis.org

0, 1, 2, 6, 16, 35, 66, 121, 203, 333, 550, 902, 1473, 2401, 3896, 6330, 10264, 16619, 26919, 43588, 70562, 114198, 184804, 299051, 483906, 783013, 1266971, 2050038, 3317059, 5367143, 8684259, 14051473, 22735799, 36787341, 59523223, 96310634, 155833920, 252144622

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, May 09 2008

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A007953, A016052, A047892, A047897-A047900, A047902, A047903, A055263, A134268, A135210, A140132.

P:=proc(n) local i,t; t:=[0,1]; for i from 1 to n do t:=[op(t),t[-2]+t[-1]+convert(convert(t[-2],base,10),`+`)+convert(convert(t[-1],base,10),`+`)]; od; print(op(t)); end: P(34); # Paolo P. Lava, Jun 25 2024

nxt[{a_,b_}]:=a+b+Total[IntegerDigits[a]]+Total[IntegerDigits[b]]; Transpose[NestList[{Last[#],nxt[#]}&,{0,1},40]][[1]] (* Harvey P. Dale, Oct 31 2011 *)

A110365 a(1)=2, a(n+1) = a(n)*A010888(a(n)).

Original entry on oeis.org

2, 4, 16, 112, 448, 3136, 12544, 87808, 351232, 2458624, 9834496, 68841472, 275365888, 1927561216, 7710244864, 53971714048, 215886856192, 1511207993344, 6044831973376, 42313823813632, 169255295254528, 1184787066781696, 4739148267126784, 33174037869887488

Offset: 1

Amarnath Murthy, Jul 24 2005

From a(2) onwards, the digital root follows the pattern alternately 4,7,4,7,4,7,...

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,28).

Cf. A010888, A047892.

k = 2; Do[Print[k]; k *= Mod[Plus @@ IntegerDigits[k], 9], {n, 1, 30}] (* Ryan Propper, Oct 13 2005 *)
LinearRecurrence[{0,28},{2,4,16},30] (* Harvey P. Dale, Mar 17 2019 *)

Vec(2*x*(1+2*x-20*x^2)/(1-28*x^2) + O(x^50)) \\ Colin Barker, May 05 2016

a(1) = 2, a(2) = 4, a(3) = 16. a(2*n) = 4*a(2*n-1), a(2*n+1) = 7*a(2*n) for n > 1.
From Colin Barker, May 05 2016: (Start)
a(n) = 2^(-1+n)*(7^(1/2*(-3+n))*(2-2*(-1)^n + sqrt(7) + (-1)^n*sqrt(7))) for n > 1.
a(n) = 2^n*7^(n/2-1) for n > 1 and even.
a(n) = 2^(n+1)*7^((n-3)/2) for n > 1 and odd.
a(n) = 28*a(n-2) for n > 3.
G.f.: 2*x*(1+2*x-20*x^2) / (1-28*x^2).
(End)
E.g.f.: (-7 + 70*x + 7*cosh(2*Sqrt(7)*x) + 2*sqrt(7)*sinh(2*sqrt(7)*x))/49. - Ilya Gutkovskiy, May 05 2016

More terms from Ryan Propper, Oct 13 2005

Name clarified by Robert Israel, May 05 2016

A140132 a(n) = Sum_digits{a(n-1)+a(n-2)+Sum_digits[a(n-1)]+Sum_digits[a(n-2)]}, with a(0)=0 and a(1)=1.

Original entry on oeis.org

0, 1, 2, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7, 8, 3, 4, 5, 9, 10, 11, 6, 7

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, May 09 2008

After the first three terms the sequence is periodic: 6,7,8,3,4,5,9,10,11.

Cf. A016052, A047892, A047897, A047898, A047899, A047900, A047902, A047903, A055263, A134268, A135210, A140131.

P:=proc(n) local a,i,t; t:=[0,1]; for i from 1 to n do
a:=t[-2]+t[-1]+convert(convert(t[-2],base,10),`+`)+convert(convert(t[-1],base,10),`+`);
t:=[op(t),convert(convert(a,base,10),`+`)]; od; print(op(t)); end: P(93); # Paolo P. Lava, Jun 25 2024

cp's OEIS Frontend

A047903 a(1) = 13; for n > 0, a(n+1) = a(n) * sum of digits of a(n).

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A140131 a(n) = a(n-1) + a(n-2) + digsum(a(n-1)) + digsum(a(n-2)), with a(0)=0 and a(1)=1.

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A110365 a(1)=2, a(n+1) = a(n)*A010888(a(n)).

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A140132 a(n) = Sum_digits{a(n-1)+a(n-2)+Sum_digits[a(n-1)]+Sum_digits[a(n-2)]}, with a(0)=0 and a(1)=1.

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