This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a = {}; b = {}; Do[AppendTo[b, n]; w =Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; If[PrimeQ[j], AppendTo[a, j]], {m, 1, Length[w]}], {n, 0, 10}]; a (*Artur Jasinski*)
for(b=2,3, for(i=0,b!-1, p=fromdigits(apply(j->j-1, numtoperm(b,i)),b); if(isprime(p), print1(p", ")))) \\ Charles R Greathouse IV, Dec 14 2015
a = {}; b = {}; Do[AppendTo[b, n]; w =Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; If[PrimeQ[j], AppendTo[a, j]], {m, 1, Length[w]}], {n, 0, 10}]; a (*Artur Jasinski*)
Select[Flatten[Table[FromDigits[#,n]&/@Permutations[Range[0,n-1]],{n,5}]],!PrimeQ[#]&] (* Harvey P. Dale, Nov 30 2023 *)
a = {}; b = {}; Do[AppendTo[b, n]; w =Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; If[OddQ[j],AppendTo[a, j]], {m, 1, Length[w]}], {n, 0, 10}]; a (*Artur Jasinski*)
a = {}; b = {}; Do[AppendTo[b, n]; w =Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; If[OddQ[j], AppendTo[a, j]], {m, 1, Length[w]}], {n, 0, 10}]; a (*Artur Jasinski*)
N:= 10^10: # for terms <= N
extend:= proc(x, N, S, b, k)
local i, R;
R:= NULL;
for i in S while x + i*b^k <= N do
if k = 0 then
if issqr(x+i*b^k) then R:= R, x+i*b^k fi
else
R:= R, procname(x+i*b^k, N, subs(i=NULL, S), b, k-1)
fi
od;
R
end proc:
f:= (b, N) -> extend(0, N, [$0..(b-1)], b, b-1):
R:= 0:
for b from 2 while b^(b-2) < N do
R:= R, f(b, N);
od:
sort([R]); # Robert Israel, Sep 04 2020
a = {}; b = {}; Do[AppendTo[b, n]; w = Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; If[IntegerQ[j^(1/2)], AppendTo[a, j]], {m, 1, Length[w]}], {n, 0, 7}]; a
N:= 10^5: # for terms <= N
extend:= proc(x,N,S,b,k)
local i,R;
R:= NULL;
for i in S while x + i*b^k <= N^2 do
if k = 0 then
if issqr(x+i*b^k) then R:= R, sqrt(x+i*b^k) fi
else
R:= R, procname(x+i*b^k,N,subs(i=NULL,S),b,k-1)
fi
od;
R
end proc:
f:= (b,N) -> extend(0,N,[$0..(b-1)],b,b-1):
R:= 0:
for b from 2 while b^(b-2) < N^2 do
R:= R, f(b,N);
od:
sort([R]); # Robert Israel, Sep 04 2020
a = {}; b = {}; Do[AppendTo[b, n]; w =Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; If[IntegerQ[j^(1/2)], AppendTo[a, j]], {m, 1, Length[w]}], {n, 0, 7}]; Sqrt[a]
a = {}; d = {}; e = {-1}; Do[b = {}; c = {}; Do[If[k > 0, AppendTo[b, k]]; AppendTo[c, n - k], {k, 0, n}] ; AppendTo[a, FromDigits[b, n + 1]]; AppendTo[d, FromDigits[c, n + 1]], {n, 1, 30}]; Do[AppendTo[e, d[[n]] - a[[n + 1]]], {n, 1, 29}]; e
a = {}; b = {}; Do[AppendTo[b, n]; w = Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; AppendTo[a, j], {m, 1, Length[w]}], {n, 0, 5}]; c = Table[n, {n, 0, 44790}]; k = Complement[c, a] (*Artur Jasinski*)
a = {}; b = {}; Do[AppendTo[b, n]; w = Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; AppendTo[a, j], {m, 1, Length[w]}], {n, 0, 5}]; d = {}; Do[AppendTo[d, a[[n + 1]] - a[[n]]], {n, 1, Length[a] - 1}] ; d (*Artur Jasinski*)
Differences[Flatten[Table[FromDigits[#,n]&/@Permutations[Range[0,n-1]], {n,5}]]] (* Harvey P. Dale, Dec 09 2014 *)
a(5) = 1234[5] (in base 5) = 1*5^3 + 2*5^2 + 3*5 + 4 = 125 + 50 + 15 + 4 = 194. a(10) = 123456789 (in base 10).
a023811 n = foldl (\val dig -> val * n + dig) 0 [0 .. n - 1] -- Reinhard Zumkeller, Aug 29 2014
[0] cat [(n^n-n^2+n-1)/(n-1)^2: n in [2..20]]; // Vincenzo Librandi, May 22 2012
0, seq((n^n-n^2+n-1)/(n-1)^2, n=2..100); # Robert Israel, Dec 13 2015
Table[Total[(#1 n^#2) & @@@ Transpose@ {Range[n - 1], Reverse@ (Range[n - 1] - 1)}], {n, 20}] (* Michael De Vlieger, Jul 24 2015 *)
Table[Sum[(b - k)*b^(k - 1), {k, b - 1}], {b, 30}] (* Clark Kimberling, Aug 22 2015 *)
Table[FromDigits[Range[0, n - 1], n], {n, 20}] (* L. Edson Jeffery, Dec 13 2015 *)
{for(i=1,18,cuo=0; for(j=1,i-1,cuo=cuo+j*i^(i-j-1)); print1(cuo,", "))} \\\ Douglas Latimer, May 16 2012
A023811(n)=if(n>1,(n^n-n^2)\(n-1)^2+1) \\ M. F. Hasler, Jan 22 2013
def a(n): return (n**n - n**2 + n - 1)//((n - 1)**2) if n > 1 else 0 print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Apr 24 2023
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