A003095 -id:A003095 - cp's OEIS frontend

A060136 Square array read by antidiagonals with T(n,k)=T(n,k-1)^2+n*T(n,k-1)+1 and T(n,0)=0.

0, 1, 0, 2, 1, 0, 5, 3, 1, 0, 26, 13, 4, 1, 0, 677, 183, 25, 5, 1, 0, 458330, 33673, 676, 41, 6, 1, 0, 210066388901, 1133904603, 458329, 1805, 61, 7, 1, 0, 44127887745906175987802, 1285739649838492213, 210066388900, 3263441, 3966

Offset: 0

Henry Bottomley, Mar 05 2001

Index entries for sequences of form a(n+1)=a(n)^2 + ...

Rows include A003095, A002065, A004019. Columns include A000004, A000012, A000027 (offset), A001844. Cf. A060137.

A101190 G.f.: A(x) = Sum_{n>=0} a(n)/2^A005187(n) * x^n = lim_{n->oo} F(n)^(1/2^n) where F(n) is defined by F(n) = F(n-1)^2 + x^(2^n-1) for n >= 1 with F(0) = 1.

Original entry on oeis.org

1, 1, -1, 5, -53, 127, -677, 2221, -61133, 205563, -1394207, 4852339, -68586849, 243751723, -1741612525, 6265913725, -363239625661, 1323861506899, -9699189175227, 35700526467479, -527987675255931, 1960112858076289, -14606721595781139, 54604708004873403

Offset: 0

Paul D. Hanna, Dec 03 2004

sign

			G.f.: A(x) = 1 + 1/2*x - 1/8*x^2 + 5/16*x^3 - 53/128*x^4 + 127/256*x^5 - 677/1024*x^6 + 2221/2048*x^7 + ... + a(n)/2^A005187(n)*x^n + ...
where 2^A005187(n) is also the denominator of [x^n] 1/sqrt(1-x).
GENERATING METHOD.
We can illustrate the generating method for g.f. A(x) as follows.
Given F(n) = F(n-1)^2 + (2*x)^(2^n-1) for n >= 1 with F(0) = 1,
the first few polynomials generated by F(n) begin
F(0) = 1,
F(1) = F(0)^2 + x^(2^1-1) = 1 + x,
F(2) = F(1)^2 + x^(2^2-1) = 1 + 2*x + x^2 + x^3,
F(3) = F(2)^2 + x^(2^3-1) = 1 + 4*x + 6*x^2 + 6*x^3 + 5*x^4 + 2*x^5 + x^6 + x^7.
...
The 2^n-th roots of F(n) tend to the limit of the g.f.:
F(1)^(1/2^1) = 1 + 1/2*x - 1/8*x^2 + 1/16*x^3 - 5/128*x^4 + 7/256*x^5 - 21/1024*x^6 + 33/2048*x^7 - 429/32768*x^8 + ...
F(2)^(1/2^2) = 1 + 1/2*x - 1/8*x^2 + 5/16*x^3 - 53/128*x^4 + 127/256*x^5 - 677/1024*x^6 + 1965/2048*x^7 - 46797/32768*x^8 + ...
F(3)^(1/2^3) = 1 + 1/2*x - 1/8*x^2 + 5/16*x^3 - 53/128*x^4 + 127/256*x^5 - 677/1024*x^6 + 2221/2048*x^7 - 61133/32768*x^8 + ...
...
The limit of this process equals the g.f. A(x) of this sequence.
Note: the sum of the coefficients in F(n) equals A003095(n):
1, 2 = 1 + 1, 5 = 1 + 2 + 1 + 1, 26 = 1 + 4 + 6 + 6 + 5 + 2 + 1 + 1, ...
The last n coefficients in F(n) read backwards are Catalan numbers (A000108).
POWERS OF A(x).
The coefficients of x^k in the 2^n powers of the g.f. A(x) begin:
A^(2^0) = [1, 1/2, -1/8, 5/16, -53/128, 127/256, -677/1024, 2221/2048, ...],
A^(2^1) = [1, 1, 0, 1/2, -1/2, 1/2, -5/8, 9/8, -2, 53/16, -89/16, 155/16, ...],
A^(2^2) = [1, 2, 1, 1, 0, 0, 0, 1/2, -1, 3/2, -5/2, 9/2, -8, 14, -197/8, 44, ...],
A^(2^3) = [1, 4, 6, 6, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1/2, -2, 5, ...],
A^(2^4) = [1, 8, 28, 60, 94, 116, 114, 94, 69, 44, 26, 14, 5, 2, 1, 1, 0, 0, ...].

Cf. A101189, A101191, A005187, A003095, A000108.

{a(n) = my(F=1,A,L); if(n==0,A=1,L=ceil(log(n+1)/log(2)); for(k=1,L, F = F^2 + x^(2^k-1) +x*O(x^n)); A = polcoeff(F^(1/2^L),n)); numerator(A)}
for(n=0,32, print1(a(n),", "))

G.f. A(x) = ( Sum_{n>=0} A101191(n)/2^A004134(n) * x^n )^2.

G.f. A(x) satisfies A(2*x)^2 = Sum_{n>=0} A101189(n)*(2*x)^n.

Entry revised by Paul D. Hanna, Mar 05 2024

A101191 G.f.: A(x) = Sum_{n>=0}a(n)/2^A004134(n)*x^n = limit_{n->oo} F(n)^(1/2^(n+1)) where F(n) is the n-th iteration of: F(0) = 1, F(n) = F(n-1)^2 + x^(2^n-1) for n>=1.

Original entry on oeis.org

1, 1, -3, 23, -525, 2695, -29687, 191991, -10488701, 70977675, -968279181, 6752850945, -191225421641, 1363019302883, -19538003443615, 140961586090743, -16379289413266717, 119621607825995891, -1755802638936696081, 12944528671963135869, -383361262914445548739

Offset: 0

Paul D. Hanna, Dec 03 2004

sign

Although the power series for the g.f. A(x) diverges at x=1, the Euler transform of the power series A(x) at x=1 converges to the constant A076949: Sum_{n>=0}[Sum_{k=0..n}C(n,k)*a(k))/2^A004134(n) ]/2^(n+1) = 1.2259024435...

			The iteration begins:
F(0) = 1,
F(1) = F(0)^2 + x^(2^1-1) = 1 +x,
F(2) = F(1)^2 + x^(2^2-1) = 1 +2*x +x^2 +x^3,
F(3) = F(2)^2 + x^(2^3-1) = 1 +4*x +6*x^2 +6*x^3 +5*x^4 +2*x^5 +x^6 +x^7.
The 2^(n+1)-th roots of F(n) tend to the limit of the g.f.:
F(1)^(1/2^2) = 1 +1/4*x -3/32*x^2 +7/128*x^3 -77/2048*x^4 +231/8192*x^5 +...
F(2)^(1/2^3) = 1 +1/4*x -3/32*x^2 +23/128*x^3 -525/2048*x^4 +2695/8192*x^5 +...
F(3)^(1/2^4) = 1 +1/4*x -3/32*x^2 +23/128*x^3 -525/2048*x^4 +2695/8192*x^5 +...
The limit of this process is the g.f. A(x) of this sequence.
The coefficients of x^k in the 2^n powers of the g.f. A(x) begin:
A^(2^0)=[1,1/4,-3/32,23/128,-525/2048,2695/8192,-29687/65536,...],
A^(2^1)=[1,1/2,-1/8,5/16,-53/128,127/256,-677/1024,2221/2048,...],
A^(2^2)=[1,1,0,1/2,-1/2,1/2,-5/8,9/8,-2,53/16,-89/16,155/16,...],
A^(2^3)=[1,2,1,1,0,0,0,1/2,-1,3/2,-5/2,9/2,-8,14,-197/8,44,...],
A^(2^4)=[1,4,6,6,5,2,1,1,0,0,0,0,0,0,0,1/2,-2,5,...],
A^(2^5)=[1,8,28,60,94,116,114,94,69,44,26,14,5,2,1,1,0,0,...].
Note: the sum of the coefficients of x^k in F(n) equals A003095(n+1):
1, 2=1+1, 5=1+2+1+1, 26=1+4+6+6+5+2+1+1, ...
The last n coefficients in F(n) read backwards are Catalan numbers (A000108).

Cf. A101189, A101190, A005187, A003095, A076949.

{a(n)=local(F=1,A,L);if(n==0,A=1,L=ceil(log(n+1)/log(2)); for(k=1,L,F=F^2+x^(2^k-1)); A=polcoeff(F^(1/2^(L+1))+x*O(x^n),n));numerator(A)}

G.f. A(x) satisfies: A(x)^2 = Sum_{n>=0} A101190(n)/2^A005187(n)*x^n. G.f. A(x) satisfies: A(2*x)^4 = Sum_{n>=0} A101189(n)*(2x)^n.

A256348 Moduli n for which A248218(n) = 8.

Original entry on oeis.org

193, 386, 461, 523, 579, 772, 887, 922, 1019, 1046, 1158, 1351, 1383, 1544, 1569, 1774, 1844, 1861, 2038, 2092, 2123, 2153, 2269, 2316, 2509, 2661, 2702, 2766, 2887, 3057, 3088, 3138, 3227, 3391, 3449, 3541, 3548, 3661, 3667, 3688, 3722, 3919

Offset: 1

M. F. Hasler, Mar 25 2015

nonn

If x and y are members, then so is LCM(x,y). - Robert Israel, Mar 08 2021

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A248218, A248219, A256342 - A256349, A003095, A247981.

filter:= proc(n) local x,k,R;
  x:= 0; R[0]:= 0;
  for k from 1 do
    x:= x^2+1 mod n;
    if assigned(R[x]) then return evalb(k-R[x] = 8)
    else R[x]:= k fi
  od;
end proc:
select(filter, [$1..5000]); # Robert Israel, Mar 08 2021

filter[n_] := Module[{x, k, R}, x = 0; R[0] = 0; For[k = 1, True, k++, x = Mod[x^2+1, n]; If[IntegerQ[R[x]], Return[k - R[x] == 8], R[x] = k]]];
Select[Range[4000], filter] (* Jean-François Alcover, May 15 2023, after Robert Israel *)

for(i=1,3000,A248218(i)==8&&print1(i","))

A293390 Least m such that the exponents in expression for n as a sum of distinct powers of 2 are pairwise distinct mod m; a(0) = 0 by convention.

Original entry on oeis.org

0, 1, 1, 2, 1, 3, 2, 3, 1, 2, 3, 4, 2, 4, 3, 4, 1, 3, 2, 5, 3, 3, 4, 5, 2, 5, 4, 5, 3, 5, 4, 5, 1, 2, 3, 3, 2, 4, 5, 6, 3, 4, 3, 6, 4, 4, 5, 6, 2, 3, 5, 6, 4, 6, 5, 6, 3, 6, 5, 6, 4, 6, 5, 6, 1, 4, 2, 4, 3, 5, 3, 7, 2, 4, 4, 4, 5, 5, 6, 7, 3, 5, 4, 7, 3, 5, 6

Offset: 0

Rémy Sigrist, Oct 08 2017

The set of exponents in expression for n as a sum of distinct powers of 2 corresponds to the n-th row of A133457.
The sum of digits of n in base 2^a(n), say s, can be computed without carry in base 2; the Hamming weight of s equals the Hamming weight of n.
a(n) >= A000120(n) for any n > 0.
Apparently, a(n) = A000120(n) iff n = 0 or n belongs to A100290.
a(n) <= A070939(n) for any n >= 0.
For any sequence s of distinct nonnegative integers (s(n) being defined for n >= 0):
- let D_s be defined for any n > 0 by D_s(n) = a(Sum_{k=0..n-1} 2^s(k)),
- then D_s is the discriminator of s as introduced by Arnold, Benkoski, and McCabe in 1985,
- D_s(1) = 1,
- D_s(n) >= n for any n >= 1,
- D_s(n+1) >= D_s(n) for any n >= 1.

			For n=42:
- 42 = 2^5 + 2^3 + 2^1,
- 5 mod 1 = 3 mod 1,
- 5 mod 2 = 3 mod 2,
- 5 mod 3, 3 mod 3 and 1 mod 3 are all distinct,
- hence a(42) = 3.

Robert Israel, Table of n, a(n) for n = 0..10000
Sajed Haque, Jeffrey Shallit, Discriminators and k-Regular Sequences, arXiv:1605.00092 [cs.DM], 2016.

Cf. A000041, A000045, A000058, A000069, A000108, A000110, A000120, A000215, A001147, A001566, A001969, A002808, A003095, A005823, A016726, A062383, A070939, A076793, A100290, A133457, A173195, A270097, A270151, A270176, A272633, A272881, A272882, A273037, A273041, A273043, A273044, A273056, A273062, A273064, A273068, A273237, A273377

f:= proc(n) local L,D,k;
  L:= convert(n,base,2);
  L:= select(t -> L[t+1]=1, [$0..nops(L)-1]);
  if nops(L) = 1 then return 1 fi;
  D:= {seq(seq(L[j]-L[i],i=1..j-1),j=2..nops(L))};
  D:= `union`(seq(numtheory:-divisors(i),i=D));
  min({$2..max(D)+1} minus D)
end proc:
0, seq(f(i),i=1..100); # Robert Israel, Oct 08 2017

{0}~Join~Table[Function[r, SelectFirst[Range@ 10, Length@ Union@ Mod[r, #] == Length@ r &]][Join @@ Position[#, 1] - 1 &@ Reverse@ IntegerDigits[n, 2]], {n, 86}] (* Michael De Vlieger, Oct 08 2017 *)

a(n) = if (n, my (d=Vecrev(binary(n)), x = []); for (i=1, #d, if (d[i], x = concat(x, i-1))); for (m=1, oo, if (#Set(vector(#x, i, x[i]%m))==#x, return (m))), return (0))

a(2*n) = a(n) for any n >= 0.
a(2^k-1) = k for any k >= 0.
a(n) = 1 iff n = 2^k for some k >= 0.
a(n) = 2 iff n belongs to A173195.
a(Sum_{k=1..n} 2^(k^2)) = A016726(n) for any n >= 1.
a(Sum_{k=1..n} 2^A000069(k)) = A062383(n) for any n >= 1.
a(Sum_{k=0..n} 2^(2^k)) = A270097(n) for any n >= 0.
a(Sum_{k=1..n} 2^A000045(k+1)) = A270151(n) for any n >= 1.
a(Sum_{k=1..n} 2^A000041(k)) = A270176(n) for any n >= 1.
a(A076793(n)) = A272633(n) for any n >= 0.
a(Sum_{k=1..n} 2^A001969(k)) = A272881(n) for any n >= 1.
a(Sum_{k=1..n} 2^A005823(k)) = A272882(n) for any n >= 1.
a(Sum_{k=1..n} 2^A000215(k-1)) = A273037(n) for any n >= 1.
a(Sum_{k=1..n} 2^A000108(k)) = A273041(n) for any n >= 1.
a(Sum_{k=1..n} 2^A001566(k)) = A273043(n) for any n >= 1.
a(Sum_{k=1..n} 2^A003095(k)) = A273044(n) for any n >= 1.
a(Sum_{k=1..n} 2^A000058(k-1)) = A273056(n) for any n >= 1.
a(Sum_{k=1..n} 2^A002808(k)) = A273062(n) for any n >= 1.
a(Sum_{k=1..n} 2^(k!)) = A273064(n) for any n >= 1.
a(Sum_{k=1..n} 2^(k^k)) = A273068(n) for any n >= 1.
a(Sum_{k=1..n} 2^A000110(k)) = A273237(n) for any n >= 1.
a(Sum_{k=1..n} 2^A001147(k)) = A273377(n) for any n >= 1.

A330405 a(1) = 0; thereafter a(n) = (a(n-1)^2+1) mod n.

Original entry on oeis.org

0, 1, 2, 1, 2, 5, 5, 2, 5, 6, 4, 5, 0, 1, 2, 5, 9, 10, 6, 17, 17, 4, 17, 2, 5, 0, 1, 2, 5, 26, 26, 5, 26, 31, 17, 2, 5, 26, 14, 37, 17, 38, 26, 17, 20, 33, 9, 34, 30, 1, 2, 5, 26, 29, 17, 10, 44, 23, 58, 5, 26, 57, 37, 26, 27, 4, 17, 18, 49, 22, 59, 26, 20, 31, 62, 45, 24

Offset: 1

Matthew Ryan, Dec 12 2019

Does the value 0 appear infinitely many times? - Rémy Sigrist, Dec 16 2019
From Michael De Vlieger, Jan 26 2020: (Start)
Observations based on a(n) for 1 <= n <= 300000:
The value 0 appears at indices n = {1, 13, 26, 89, 205, 530, 2041, 276205, ...}.
The value 1 appears at indices n = {2, 4, 14, 27, 50, 90, 99, 175, 188, 206, 531, 2042, 5445, 6845, 7200, 18225, 24389, 25215, 37538, 46875, 48672, 53066, 79527, 93900, 147875, 176267, 186576, 196025, 254457, 276206, ...}. Let M be the indices in a(n) where 1 appears.
The subsequence {1, 2, 5, 26} appears with the first term at index n = 27, and apparently for all subsequent indices listed n M.
The subsequence {1, 2, 5, 26, 677} appears with the first term at index n = 2042, and apparently for all subsequent indices listed n M.
A stable next term in the subsequence S = {1, 2, 5, 26, 677} is not yet apparent, given 300000 terms of a(n). (End)

			a(1) = 0; a(2) = (0^2+1) mod 2 = 1; a(3) = (1^2+1) mod 2 = 2.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A003095, A064434.

Nest[Append[#1, Mod[#1[[#2 - 1]]^2 + 1, #2]] & @@ {#, Length@ # + 1} &, {0}, 76] (* Michael De Vlieger, Dec 16 2019 *)

v=0; for (n=1, 77, print1 (v=(v^2+1)%n", ")) \\ Rémy Sigrist, Dec 16 2019

a(1) = 0; a(n) = (a(n-1)^2+1) mod n.

A332965 a(n) is the number of distinct values in the sequence s defined by s(1) = 0 and for any k > 0, s(k+1) = (s(k)^2+1) mod n.

Original entry on oeis.org

1, 2, 3, 3, 3, 4, 4, 4, 5, 6, 6, 4, 4, 5, 5, 5, 8, 8, 6, 7, 4, 6, 8, 4, 4, 4, 5, 5, 11, 8, 5, 5, 6, 8, 6, 8, 6, 7, 6, 8, 7, 5, 8, 6, 5, 8, 14, 5, 9, 7, 8, 5, 9, 8, 10, 5, 6, 11, 11, 8, 15, 6, 6, 6, 12, 6, 12, 8, 8, 9, 18, 8, 9, 7, 5, 7, 6, 6, 8, 9, 11, 14, 11

Offset: 1

Rémy Sigrist, Mar 04 2020

nonn

For any n > 0, the sequence s is eventually periodic, so this sequence is well defined.

a(n) tends to infinity as n tends to infinity.

			For n = 42:
- we have:
  k  s(k)
  -  ----
  1     1
  2     2
  3     5
  4    26
  5     5
  6    26
  ...
- the sequence s has 4 distinct values, so a(42) = 4.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A003095, A332966.

a(n) = { my (s=0, v=0, w=0); while (!bittest(w,s), w+=2^s; v++; s=(s^2+1)%n); v }

a(n) > k for any k >= 0 and n > A003095(k).

A332966 a(n) is the largest value in the sequence s defined by s(1) = 0 and for any k > 0, s(k+1) = (s(k)^2+1) mod n.

Original entry on oeis.org

0, 1, 2, 2, 2, 5, 5, 5, 8, 7, 6, 5, 5, 12, 11, 10, 16, 17, 12, 17, 5, 17, 13, 5, 5, 5, 26, 26, 26, 26, 26, 26, 26, 33, 26, 29, 26, 31, 26, 37, 32, 26, 36, 26, 26, 33, 43, 26, 47, 30, 50, 26, 41, 53, 50, 26, 50, 50, 30, 50, 53, 57, 47, 37, 57, 26, 56, 65, 59

Offset: 1

Rémy Sigrist, Mar 04 2020

nonn

For any n > 0, the sequence s is eventually periodic, so this sequence is well defined.

a(n) tends to infinity as n tends to infinity.

			For n = 42:
- we have:
  k  s(k)
  -  ----
  1     1
  2     2
  3     5
  4    26
  5     5
  6    26
  ...
- the sequence s has largest value 26, so a(42) = 26.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of the first 750000 terms

Cf. A003095, A248218, A330405, A332965.

a(n) = { my (s=0, v=s, w=0); while (!bittest(w,s), w+=2^s; v=max(v,s); s=(s^2+1)%n); v }

a(n) >= A003095(k) for any k >=0 and n > A003095(k).

A060137 Square array read by antidiagonals with T(n,k)=T(n,k-1)^2-n*T(n,k-1)+1 and T(n,0)=0.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 5, 1, 1, 0, 26, 1, 0, 1, 0, 677, 1, 1, -1, 1, 0, 458330, 1, 0, 5, -2, 1, 0, 210066388901, 1, 1, 11, 13, -3, 1, 0, 44127887745906175987802, 1, 0, 89, 118, 25, -4, 1, 0, 1947270476915296449559703445493848930452791205, 1, 1, 7655, 13453, 501, 41, -5, 1, 0

Offset: 0

Henry Bottomley, Mar 05 2001

Index entries for sequences of form a(n+1)=a(n)^2 + ...

Rows include A003095, A057427, A000035. Columns include A000004, A000012, A022958, A001844 (offset). Cf. A060136.

T(0,k)=A004019(k-1)+1=A056207(k-2)+2. - R. J. Mathar, Apr 24 2007

A135361 a(n) = a(n-1)^3 + 1 with a(0) = 0.

Original entry on oeis.org

0, 1, 2, 9, 730, 389017001, 58871587162270593034051002, 204040901322752673844230437877671861543858084850895762746141813554591014612009

Offset: 0

Gerald McGarvey, Dec 08 2007

Number of ternary trees of height less than n.

The rightmost digits cycle (0, 1, 2, 9, 0, 1, 2, 9, ...).

Michael De Vlieger, Table of n, a(n) for n = 0..9
Robin Lamarche-Perrin, An Information-theoretic Framework for the Lossy Compression of Link Streams, arXiv:1807.06874 [cs.DS], 2018.
C. Lenormand, Arbres et permutations, 1.2: Magmas et Arborescences, pp. 55, 57.

Cf. A003095, A008322, A119731.

Nest[Append[#, #[[-1]]^3 + 1] &, {0}, 7] (* Michael De Vlieger, Oct 24 2018 *)

def a(n): return 0 if (n==0) else a(n-1)^3 + 1
[a(n) for n in (0..9)] # G. C. Greubel, Jul 19 2021

a(n) is asymptotic to c^(3^n) where c=1.0847999710783722816939038440390528005339362697...

cp's OEIS Frontend

A060136 Square array read by antidiagonals with T(n,k)=T(n,k-1)^2+n*T(n,k-1)+1 and T(n,0)=0.

Views

Author

Keywords

Links

Crossrefs

A101190 G.f.: A(x) = Sum_{n>=0} a(n)/2^A005187(n) * x^n = lim_{n->oo} F(n)^(1/2^n) where F(n) is defined by F(n) = F(n-1)^2 + x^(2^n-1) for n >= 1 with F(0) = 1.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Formula

Extensions

A101191 G.f.: A(x) = Sum_{n>=0}a(n)/2^A004134(n)*x^n = limit_{n->oo} F(n)^(1/2^(n+1)) where F(n) is the n-th iteration of: F(0) = 1, F(n) = F(n-1)^2 + x^(2^n-1) for n>=1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Formula

A256348 Moduli n for which A248218(n) = 8.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A293390 Least m such that the exponents in expression for n as a sum of distinct powers of 2 are pairwise distinct mod m; a(0) = 0 by convention.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A330405 a(1) = 0; thereafter a(n) = (a(n-1)^2+1) mod n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A332965 a(n) is the number of distinct values in the sequence s defined by s(1) = 0 and for any k > 0, s(k+1) = (s(k)^2+1) mod n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A332966 a(n) is the largest value in the sequence s defined by s(1) = 0 and for any k > 0, s(k+1) = (s(k)^2+1) mod n.

Views

Author

Keywords

Comments

Examples