A013716 -id:A013716 - cp's OEIS frontend

A013715 a(n) = 10^(2*n+1).

10, 1000, 100000, 10000000, 1000000000, 100000000000, 10000000000000, 1000000000000000, 100000000000000000, 10000000000000000000, 1000000000000000000000, 100000000000000000000000, 10000000000000000000000000, 1000000000000000000000000000, 100000000000000000000000000000

Offset: 0

N. J. A. Sloane

Bisection of A011557 (powers of 10). - Michel Marcus, Jan 17 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (100).

Cf. A013708-A013714, A013716-A013729, A011557.

Cf. A005408, A098608, A013747.

[10^(2*n+1): n in [0..20]]; // Vincenzo Librandi, Jun 26 2011

seq(10^(2*n+1),n=0..11); # Nathaniel Johnston, Jun 25 2011

10^(2 Range[0, 15] + 1) (* Wesley Ivan Hurt, Jan 17 2016 *)

a(n) = 10^(2*n+1); \\ Michel Marcus, Jan 17 2016

Vec(10/(1-100*x) + O(x^100)) \\ Altug Alkan, Jan 17 2016

From Philippe Deléham, Nov 25 2008: (Start)
G.f.: 10/(1-100*x).
a(n) = 100*a(n-1), n>0; a(0)=10. (End)
From Elmo R. Oliveira, Aug 26 2024 (Start)
E.g.f.: 10*exp(100*x).
a(n) = 10*A098608(n) = A011557(A005408(n)) = A013747(n)/10^(n+1). (End)

A262715 a(n) = 29^(2*n+1).

Original entry on oeis.org

29, 24389, 20511149, 17249876309, 14507145975869, 12200509765705829, 10260628712958602189, 8629188747598184440949, 7257147736730073114838109, 6103261246589991489578849669, 5132842708382182842735812571629, 4316720717749415770740818372739989

Offset: 0

Vincenzo Librandi, Oct 02 2015

29*a(n) is a square.

G. C. Greubel, Table of n, a(n) for n = 0..250
Index entries for linear recurrences with constant coefficients, signature (841).

Second bisection of A009973 (powers of 29).

Cf. similar sequences of the form p^(2*n+1), with p prime: A004171 (p=2), A013708 (p=3), A013710 (p=5), A013712 (p=7), A013716 (p=11), A013718 (p=13), A013722 (p=17), A013724 (p=19), A013728 (p=23), this sequence (p=29), A262716 (p=31), A262786 (p=37), A262787 (p=41), A155477 (p=43).

Magma
```
[29^(2*n+1): n in [0..15]];
```

29^Range[1, 30, 2]
NestList[841#&,29,20] (* Harvey P. Dale, May 16 2025 *)

vector(20, n, n--; 29^(2*n+1)) \\ Altug Alkan, Oct 02 2015

G.f.: 29/(1 - 841*x).
a(n) = 841*a(n-1).
Sum_{i>=0} (-1)^i/a(i) = 29*A021846; Sum_{i>=0} 1/a(i) = 2.9*A021088. [Bruno Berselli, Oct 06 2015]

A013717 a(n) = 12^(2*n + 1).

Original entry on oeis.org

12, 1728, 248832, 35831808, 5159780352, 743008370688, 106993205379072, 15407021574586368, 2218611106740436992, 319479999370622926848, 46005119909369701466112, 6624737266949237011120128

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (144).

Bisection of A001021.

Cf. A013708-A013716, A013718-A013729.

[12^(2*n+1): n in [0..15]]; // Vincenzo Librandi, Jun 26 2011

seq(12^(2*n+1),n=0..11); # Nathaniel Johnston, Jun 25 2011

a(n)=12^(2*n+1) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 25 2008: (Start)
a(n) = 144*a(n-1), a(0)=12.
G.f.: 12/(1-144*x). (End)

A013727 a(n) = 22^(2*n + 1).

Original entry on oeis.org

22, 10648, 5153632, 2494357888, 1207269217792, 584318301411328, 282810057883082752, 136880068015412051968, 66249952919459433152512, 32064977213018365645815808, 15519448971100888972574851072, 7511413302012830262726227918848, 3635524038174209847159494312722432

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (484).

Bisection of A009966 (22^n).

Cf. A004171, A005408, A013708-A013726, A013728-A013729.

[22^(2*n+1): n in [0..15]]; // Vincenzo Librandi, Jun 26 2011

seq(22^(2*n+1),n=0..10); # Nathaniel Johnston, Jun 26 2011

NestList[484*# &, 22, 15] (* Paolo Xausa, Jul 12 2025 *)

a(n)=22^(2*n+1) \\ Charles R Greathouse IV, Jul 11 2016

From Philippe Deléham, Nov 28 2008: (Start)
a(n) = 484*a(n-1); a(0)=22.
G.f.: 22/(1-484*x). (End)
From Elmo R. Oliveira, Jul 10 2025: (Start)
E.g.f.: 22*exp(484*x).
a(n) = A004171(n)*A013716(n) = A009966(A005408(n)). (End)

cp's OEIS Frontend

A013715 a(n) = 10^(2*n+1).

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A262715 a(n) = 29^(2*n+1).

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A013717 a(n) = 12^(2*n + 1).

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Maple

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A013727 a(n) = 22^(2*n + 1).

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Magma

Maple

Mathematica

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