A074611 -id:A074611 - cp's OEIS frontend

A045590 Numbers k that divide 5^k + 4^k.

1, 3, 9, 21, 27, 63, 81, 147, 189, 243, 441, 567, 729, 903, 1029, 1323, 1701, 2187, 2667, 2709, 2943, 3087, 3969, 5103, 6321, 6561, 7203, 8001, 8127, 8829, 9261, 11907, 13203, 15309, 18669, 18963, 19683, 20601, 21609, 24003, 24381, 26487

Offset: 1

David W. Wilson

nonn

From Robert Israel, May 19 2025: (Start)
All terms are coprime to 10.
The only prime term is 3.
If k is a term, then so is 3 * k.
Is 1 the only term not divisible by 3? (End)

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A074611.

filter:= k -> 5 &^ k + 4 &^ k mod k = 0:
select(filter, [seq(i,i=1..10^5,2)]); # Robert Israel, May 19 2025

Select[Range[30000],Divisible[5^#+4^#,#]&] (* Harvey P. Dale, Nov 17 2013 *)

A210694 T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.

Original entry on oeis.org

5, 13, 9, 25, 35, 17, 41, 91, 97, 33, 61, 189, 337, 275, 65, 85, 341, 881, 1267, 793, 129, 113, 559, 1921, 4149, 4825, 2315, 257, 145, 855, 3697, 10901, 19721, 18571, 6817, 513, 181, 1241, 6497, 24583, 62281, 94509, 72097, 20195, 1025, 221, 1729, 10657, 49575

Offset: 1

R. H. Hardin, with R. J. Mathar in the Sequence Fans Mailing List, Mar 30 2012

Table starts
...5....13.....25......41.......61.......85.......113.......145........181
...9....35.....91.....189......341......559.......855......1241.......1729
..17....97....337.....881.....1921.....3697......6497.....10657......16561
..33...275...1267....4149....10901....24583.....49575.....91817.....159049
..65...793...4825...19721....62281...164305....379793....793585....1531441
.129..2315..18571...94509...358061..1103479...2920695...6880121...14782969
.257..6817..72097..456161..2070241..7444417..22542017..59823937..143046721
.513.20195.281827.2215269.12030821.50431303.174571335.521638217.1387420489
Solutions are determined by the diagonal, extended with x(i,j) = (x(i,i)+x(j,j))/2 * (-1)^(i-j)

			Some solutions for n=3 k=4
.-2..1.-3..0....0.-1..0..1....4..0..1.-1....2.-1.-1.-2....3.-2..1..0
..1..0..2..1...-1..2.-1..0....0.-4..3.-3...-1..0..2..1...-2..1..0.-1
.-3..2.-4..1....0.-1..0..1....1..3.-2..2...-1..2.-4..1....1..0.-1..2
..0..1..1..2....1..0..1.-2...-1.-3..2.-2...-2..1..1..2....0.-1..2.-3

R. H. Hardin, Table of n, a(n) for n = 1..10000

cf. A179927
Column 1 is A000051(n+1)
Column 2 is A007689(n+1)
Column 3 is A074605(n+1)
Column 4 is A074611(n+1)
Column 5 is A074615(n+1)
Column 6 is A074619(n+1)
Column 7 is A074622(n+1)
Column 8 is A074624(n+1)
Row 1 is A001844
Row 2 is A005898
Row 3 is A008514
Row 4 is A008515
Row 5 is A008516
Row 6 is A036085
Row 7 is A036086
Row 8 is A036087

T(n,k)=k^(n+1)+(k+1)^(n+1)

A221904 a(n) = 9^n + 10^n.

Original entry on oeis.org

2, 19, 181, 1729, 16561, 159049, 1531441, 14782969, 143046721, 1387420489, 13486784401, 131381059609, 1282429536481, 12541865828329, 122876792454961, 1205891132094649, 11853020188851841

Offset: 0

Vincenzo Librandi, Feb 06 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (19,-90).

Cf. A007689, A074611, A074615, A074619, A074622, A074624, A155872.

Magma
```
[9^n + 10^n: n in [0..30]];
```

CoefficientList[Series[1/(1-9*x) + 1/(1-10*x), {x, 0, 30}], x]
LinearRecurrence[{19,-90},{2,19},30] (* Harvey P. Dale, Nov 10 2017 *)

G.f.: 1/(1 - 9*x) + 1/(1 - 10*x).
E.g.f.: exp(9*x) + exp(10*x).
a(n) = 19*a(n-1) - 90*a(n-2), a(1)=2, a(2)=19.

cp's OEIS Frontend

A045590 Numbers k that divide 5^k + 4^k.

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A210694 T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero.

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Comments

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Crossrefs

Formula

A221904 a(n) = 9^n + 10^n.

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Author

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Crossrefs

Programs

Magma

Mathematica

Formula