A064756
a(n) = n*10^n - 1.
Original entry on oeis.org
9, 199, 2999, 39999, 499999, 5999999, 69999999, 799999999, 8999999999, 99999999999, 1099999999999, 11999999999999, 129999999999999, 1399999999999999, 14999999999999999, 159999999999999999, 1699999999999999999, 17999999999999999999, 189999999999999999999, 1999999999999999999999
Offset: 1
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Paul Leyland, Factors of Cullen and Woodall numbers.
- Paul Leyland, Generalized Cullen and Woodall numbers.
- Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.
- Index entries for linear recurrences with constant coefficients, signature (21,-120,100).
Cf. for a(n) = n*k^n - 1: -
A000012 (k=0),
A001477 (k=1),
A003261 (k=2),
A060352 (k=3),
A060416 (k=4),
A064751 (k=5),
A064752 (k=6),
A064753 (k=7),
A064754 (k=8),
A064755 (k=9), this sequence (k=10),
A064757 (k=11),
A064758 (k=12).
-
[ n*10^n-1: n in [1..20]]; // Vincenzo Librandi, Sep 16 2011
-
k:= 10; f:= gfun:-rectoproc({1 + (k-1)*n + k*n*a(n-1) - (n-1)*a(n) = 0, a(1) = k-1}, a(n), remember): map(f, [$1..20]); # Georg Fischer, Feb 19 2021
-
Array[# 10^# - 1 &, 18] (* Michael De Vlieger, Jan 14 2020 *)
A064749
a(n) = n*11^n + 1.
Original entry on oeis.org
1, 12, 243, 3994, 58565, 805256, 10629367, 136410198, 1714871049, 21221529220, 259374246011, 3138428376722, 37661140520653, 448795257871104, 5316497670165375, 62658722541234766, 735195677817154577, 8592599484487994108, 100078511642860166659, 1162022718519876379530
Offset: 0
For a(n)=n*k^n+1:
A000012 (k=0),
A000027(n+1) (k=1),
A002064 (k=2),
A050914 (k=3),
A050915 (k=4),
A050916 (k=5),
A050917 (k=6),
A050919 (k=7),
A064746 (k=8),
A064747 (k=9),
A064748 (k=10), this sequence (k=11),
A064750 (k=12).
-
[n*11^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011
-
k:= 11; f:= gfun:-rectoproc({-1 - (k-1)*n + k*n*a(n-1) - (n-1)*a(n) = 0, a(0) = 1, a(1) = k+1}, a(n), remember): map(f, [$0..20]); # Georg Fischer, Feb 19 2021
A216376
Semiprimes of the form n*10^n + 1.
Original entry on oeis.org
201, 500001, 130000000000001, 280000000000000000000000000001, 340000000000000000000000000000000001, 36000000000000000000000000000000000001, 39000000000000000000000000000000000000001
Offset: 1
a(1) = 2 * 10^2 + 1 = 201 = 3 * 67.
a(2) = 5 * 10^5 + 1 = 500001 = 3 * 166667.
a(3) = 13*10^13 + 1 = 130000000000001 = 6529 * 19911165569.
a(4) = 28 * 10^28 + 1 = 29 * 9655172413793103448275862069.
-
IsSemiprime:= func; [s: n in [1..40] | IsSemiprime(s) where s is n*10^n + 1]; // Vincenzo Librandi, Sep 22 2012
-
SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Table[n*10^n + 1, {n, 50}], SemiPrimeQ[#] &] (* T. D. Noe, Sep 07 2012 *)
Select[Table[n*10^n + 1, {n, 50}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)
A216378
Numbers m such that m*10^m + 1 is a semiprime.
Original entry on oeis.org
2, 5, 13, 28, 34, 36, 39, 111, 117, 123, 181, 184, 187
Offset: 1
a(1) = 2 because 2 * 10^2 + 1 = 201 = 3 * 67.
a(2) = 5 because 5 * 10^5 + 1 = 500001 = 3 * 166667.
a(3) = 13 because 13*10^13 + 1 = 130000000000001 = 6529 * 19911165569.
a(4) = 28 because 28 * 10^28 + 1 = 29 * 9655172413793103448275862069.
Cf. similar sequences listed in
A242203.
-
IsSemiprime:=func; [n: n in [1..70] | IsSemiprime(s) where s is n*10^n+1]; // Vincenzo Librandi, May 10 2014
-
Select[Range[40], PrimeOmega[# 10^# + 1] == 2 &] (* Alonso del Arte, Sep 08 2012 *)
A175188
Composite numbers of the form k*10^k + 1.
Original entry on oeis.org
201, 40001, 500001, 6000001, 70000001, 800000001, 100000000001, 1100000000001, 12000000000001, 130000000000001, 1400000000000001, 15000000000000001, 160000000000000001, 1700000000000000001, 18000000000000000001, 190000000000000000001, 2000000000000000000001
Offset: 1
For k=2, 2*10^2 + 1 = 201 = 3*67.
For k=4, 4*10^4 + 1 = 40001 = 13*17*181.
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
-
with(numtheory):for k from 1 to 100 do: n:=k*10^k +1:if type(n,prime) = false then print(n):else fi:od:
-
Select[Table[k*10^k+1, {k, 1, 20}], CompositeQ] (* Amiram Eldar, Aug 14 2023 *)
a(16)-a(17) added and name corrected by
Amiram Eldar, Aug 14 2023
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