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A250408
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Palindromic in bases 10 and 20.
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21
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 252, 6556, 6776, 7117, 10101, 12621, 20202, 22722, 30303, 1784871, 1786871, 1788871, 1913191, 1915191, 1917191, 1919191, 1444884441, 334495594433, 334843348433, 355110011553, 355746647553, 10614366341601, 14102600620141, 28095922959082, 38072044027083
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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MATHEMATICA
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palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; genPal[n_] := Block[{id = IntegerDigits@ n, insert = {{}, {0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}}}, FromDigits@ Join[id, #, Reverse@ id] & /@ insert]; k = 1; lst = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; While[k < 1000001, s = Select[ genPal[k], palQ[#, 20] &]; If[s != {}, AppendTo[lst, s]; Print@ s; lst = Sort@ Flatten@ lst]; k++]; lst
b1=10; b2=20; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Nov 23 2014 *)
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PROG
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(Magma) [n: n in [0..10000000] | Intseq(n, 10) eq Reverse(Intseq(n, 10))and Intseq(n, 20) eq Reverse(Intseq(n, 20))]; // Vincenzo Librandi, Nov 23 2014
(Python)
from gmpy2 import digits
def palQ(n, b): # check if n is a palindrome in base b
s = digits(n, b)
return s == s[::-1]
def palQgen10(l): # unordered generator of palindromes of length <= 2*l
if l > 0:
yield 0
for x in range(1, 10**l):
s = str(x)
yield int(s+s[-2::-1])
yield int(s+s[::-1])
A250408_list = sorted([n for n in palQgen10(6) if palQ(n, 20)])
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CROSSREFS
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Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250409, A250410, A250411, A099165, A250412.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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