A089182
Prime digit palindromes 2,...,23577532 continued by adding 10^(n-k) and 10^(k-1) times prime(k).
Original entry on oeis.org
2, 22, 232, 2332, 23532, 235532, 2357532, 23577532, 235817532, 2358217532, 23582417532, 235824417532, 2358248417532, 23582488417532, 235824908417532, 2358249108417532, 23582491508417532, 235824915508417532
Offset: 1
-
a[m_]=Delete[Table[If [ Floor[m/2]-n>=0, Prime[ n], Prime[m-n]], {n, 1, m}], m] b=Table[Sum[a[m][[i]]*10^(i-1), {i, 1, m-1}], {m, 2, digits}]
A089174
A nonsense sequence (not well-defined).
Original entry on oeis.org
2, 3, 7, 11, 13, 17, 19, 23, 37, 41, 59, 73, 101, 137, 157, 239, 257, 271, 547, 2153, 2251, 4649, 7309, 9091, 19697, 21683, 94331, 333667, 928163, 3324301, 4403881, 7532639, 8983031, 10901027, 1111211111, 11195538763, 139381546141, 1102732004467
Offset: 1
A007907 = {1, 11, 121, 1221, 12321, 123321, ...} which factor as {(1^1), (11^1), (11^2), (3^1, 11^1, 37^1), (3^2, 37^2), (3^1, 11^1, 37^1, 101^1), ...}. The list of the factors and their powers, flattened, begins as {1, 1, 11, 1, 11, 2, 3, 1, 11, 1, 37, 1, 3, 2, 37, 2, ...}. The list of ordered prime values begins as {2, 3, 7, 11, ...}.
-
digits=30;
f[m_]= Table[If[Floor[m/2]>=n, Mod[n, 10], Mod[m-n, 10]], {n,m}];
A007907= Table[Sum[f[m][[i]]*10^(i-1), {i,m}], {m, digits}];
c= Flatten[Table[FactorInteger[A007907[[n]]], {n, digits-1}]];
Rest@Union[Table[If[PrimeQ[c[[n]]], c[[n]], 1], {n, Dimensions[c][[1]]}]]
A089183
Palindromes in which, in the first half of the number, digits appear in the order 1, 0, 2, 3, 1, 0, 2, 3, 1, ...
Original entry on oeis.org
1, 11, 101, 1001, 10201, 102201, 1023201, 10233201, 102313201, 1023113201, 10231013201, 102310013201, 1023102013201, 10231022013201, 102310232013201, 1023102332013201, 10231023132013201, 102310231132013201
Offset: 1
-
digits=50 c={1, 0, 2, 3} a[m_]=Delete[Table[If [ Floor[m/2]-n>=0, c[[ Mod[n, 4]]], c[[Mod[m-n, 4]]]], {n, 1, m}], m] b=Table[Sum[a[m][[i]]*10^(i-1), {i, 1, m-1}], {m, 2, digits}]
A089184
A coding semi-palindromic sequence made by converting a zero containing limited digit set palindromic sequence to a fraction and then converting back to an continued fraction array and making the sequence up from the result.
Original entry on oeis.org
1, 22, 111, 4444, 33333, 333333, 3333333, 13333133, 133331133, 3323333233, 31133331133, 333343333433, 3333333333333, 33333333333333, 333333333333333, 3313333333313333, 31133333333113333, 333323333333323333
Offset: 2
-
Clear [a, b, c, d, e, f, g, m] (* these continued fraction functions are given in the Mathematica documentation*) CF[r0_?NumericQ, n_Integer?NonNegative] := Module[{l = {}, r = r0, a}, Do[ a = Floor[r]; (* integer part *) AppendTo[l, a]; r = r - a; (* fractional part; 0 <= r < 1 *) If[ r == 0, Break[] ]; r = 1/r; (* r > 1 *), {n}]; l ] CFValue[l_List] := Fold[ 1/#1 + #2&, Infinity, Reverse[l] ] digits=50 c[1]=1 c[2]=0 c[3]=2 c[0]=3 (* general Palindromic continued fraction generator for length m-1*) a[m_]=Delete[Table[If [ Floor[m/2]-n>=0, c[ Mod[n, 4]], c[Mod[m-n, 4]]], {n, 1, m}], m] (* make the fraction from the palindromic array*) e=Table[CFValue[Flatten[Table[a[m], {k, 1, digits}]]], {m, 2, digits}]; (* get the new semi- Palindromic continued fraction array with zeros eliminated*) f[n_]=CF[e[[n]], digits]; (* create new semi-palindromic sequence from the continued fraction array*) g=Table[Sum[f[m][[i]]*10^(i-1), {i, 1, m-1}], {m, 2, digits-1}]
A287295
a(2n-1) is concatenation of sequence (1,3,..,2n-3,2n-1,2n-3,..3,1) and a(2n) is concatenation of sequence (1,3,..,2n-3,2n-1,2n-1,2n-3,..3,1).
Original entry on oeis.org
1, 11, 131, 1331, 13531, 135531, 1357531, 13577531, 135797531, 1357997531, 135791197531, 13579111197531, 1357911131197531, 135791113131197531, 13579111315131197531, 1357911131515131197531, 135791113151715131197531, 13579111315171715131197531
Offset: 1
-
Block[{nn = 18, s}, s = IntegerDigits@ Range[1, nn, 2]; Table[FromDigits@ Flatten@ Join[#, Reverse[If[EvenQ@ n, #, Most@ #] &@ #]] &@ Take[s, Ceiling[n/2]], {n, nn}]] (* Michael De Vlieger, May 23 2017 *)
Showing 1-5 of 5 results.
Comments