A116993
a(n) is the least number having exactly n representations as a product of two palindromes.
Original entry on oeis.org
13, 1, 4, 44, 66, 484, 4444, 7326, 6666, 48884, 73326, 493284, 888888, 666666, 5426124, 4888884, 6672666, 7333326, 44888844, 73399326, 246888642, 67333266, 4073662593, 4893772884, 4533773244, 6800659866, 2715775062, 1481331852, 493777284, 740665926, 8147325186, 5431550124, 74807258526
Offset: 0
a(0)=13 since 13 is the smallest number that cannot be represented as a product of two palindromes.
a(5)=484 since 484 = 1*484 = 2*242 = 4*121 = 22*22 = 11*44.
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f[n_]:=f[n]=Length[Select[Divisors[n], #<=n^(1/2)&&FromDigits[ Reverse[IntegerDigits[ # ]]]==#&&FromDigits[Reverse[IntegerDigits [n/# ]]]==n/#&]]; a[n_]:=(For[m=1, f[m] != n, m++ ]; m); Do[Print[a[n]], {n, 0, 18}] (* Farideh Firoozbakht, Dec 10 2006 *)
A152572
Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 5^(n - 1), T(n,k) = -5^(n - k - 1), 1 <= k <= n - 1.
Original entry on oeis.org
-1, 1, -1, 5, -1, -1, 25, -5, -1, -1, 125, -25, -5, -1, -1, 625, -125, -25, -5, -1, -1, 3125, -625, -125, -25, -5, -1, -1, 15625, -3125, -625, -125, -25, -5, -1, -1, 78125, -15625, -3125, -625, -125, -25, -5, -1, -1, 390625, -78125, -15625, -3125, -625, -125, -25, -5, -1, -1
Offset: 0
Triangle begins:
-1;
1, -1;
5, -1, -1;
25, -5, -1, -1;
125, -25, -5, -1, -1;
625, -125, -25, -5, -1, -1;
3125, -625, -125, -25, -5, -1, -1;
15625, -3125, -625, -125, -25, -5, -1, -1;
78125, -15625, -3125, -625, -125, -25, -5, -1, -1;
390625, -78125, -15625, -3125, -625, -125, -25, -5, -1, -1;
1953125, -390625, -78125, -15625, -3125, -625, -125, -25, -5, -1, -1;
...
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b[0] = {-1}; b[1] = {1, -1};
b[n_] := b[n] = Join[{5^(n - 1)}, {-b[n - 1][[1]]}, Table[b[n - 1][[i]], {i, 2, Length[b[n - 1]]}]];
Flatten[Table[b[n], {n, 0, 10}]]
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T(n, k) := if k = n then -1 else if k = 0 then 5^(n - 1) else -5^(n - k - 1);
create_list(T(n, k), n, 0, 20, k, 0, n); /* Franck Maminirina Ramaharo, Jan 08 2019 */
A125832
Numbers k which have exactly 14 representations as a product of two palindromes.
Original entry on oeis.org
5426124, 8139186, 20017998, 21999978, 26690664, 26888862, 29333304, 49821684, 73267326, 97689768, 98666568, 146534652, 147999852, 220197978, 271333062, 274019262, 320221902, 403696293, 471535064, 489372884, 516019504, 518221704
Offset: 1
26888862 is in the sequence since 26888862 =
1*26888862 = 2*13444431 = 11*2444442 = 22*1222221 = 111*242242 = 121*222222 = 222*121121 =
242*111111 = 1001*26862 = 1221*22022 = 1331*20202 = 2002*13431 = 2442*11011 = 2662*10101.
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f[n_]:=f[n]=Length[Select[Divisors[n],#<=n^(1/2)&&FromDigits[ Reverse[IntegerDigits[ # ]]]==#&&FromDigits[Reverse[IntegerDigits [n/# ]]]==n/#&]];Do[If[f[n]==14,Print[n]],{n,50000000}]
A125834
Numbers that have exactly 15 representations as a product of two palindromes.
Original entry on oeis.org
4888884, 8896888, 13345332, 74732526, 100999899, 140732592, 179555376, 269130862, 295777482, 444888444, 734059326, 880968088, 978745768, 1032039008, 1183109928, 1321452132, 1399939992, 1548058512, 1614785172, 1886140256
Offset: 1
4888884 is in the sequence since 4888884 = 1*4888884 = 2*2444442 = 4*1222221 = 11*444444 = 22*222222 = 44*111111 = 111*44044 = 121*40404 = 222*22022 = 242*20202 = 444*11011 = 484*10101 = 1001*4884 = 1221*4004 = 2002*2442.
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f[n_]:=f[n]=Length[Select[Divisors[n],#<=n^(1/2)&&FromDigits[ Reverse[IntegerDigits[ # ]]]==#&&FromDigits[Reverse[IntegerDigits [n/# ]]]==n/#&]];Do[If[f[n]==15,Print[n]],{n,125000000}]
Showing 1-4 of 4 results.
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