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A293925 Triangle read by rows T(n, k) is the least integer that is a palindrome in base n and k, with more than 1 digit in both bases, n >= 3 and 2 <= k < n. 1
6643, 5, 10, 31, 26, 46, 7, 28, 21, 67, 85, 8, 85, 24, 92, 9, 121, 63, 18, 154, 121, 127, 10, 10, 109, 80, 40, 154, 33, 121, 55, 88, 55, 121, 121, 191, 255, 244, 255, 12, 166, 24, 36, 60, 232, 65, 13, 65, 26, 104, 78, 65, 91, 181, 277, 313, 28, 42, 98, 14, 235, 154, 70, 222, 84, 326 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

From Robert G. Wilson v, Nov 17 2017: (Start)

min t(n, k) by k beginning with n=3: 2, 2, 3, 2, 3, 2, 3, 2, 5, 3, 6, 2, 3, 2, 5, 4, 3, 2, 10, 3, 5, 4, 3, 2, 3, 4, 9, 2, 7, 2, ..., ;

max t(n, k) by k beginning with n=3: 2, 3, 4, 5, 6, 6, 8, 9, 2, 11, 12, 3, 5, 12, 6, 3, 18, 7, 4, 19, 8, 6, 22, 4, 2, 7, 12, 9, ..., .

(End)

Record values: 6643, 9686, 9902, 16008, 20512, 33577, 33621, 40243, 47723, 55155, 56115, 65347, 65883, 73606, 120250, 248833, 620832, 648170, 694314, 44838080, 2000608059, 4045926645, 25594427566, 37939766550, ..., . - Robert G. Wilson v, Jun 19 2021

Conjecture: for every pair of bases n and k, there exists a unique, nonempty set of solutions. - Jack Neubecker, Jun 28 2021

LINKS

Michel Marcus, Rows 3..100 of triangle, flattened

Jean-Paul Delahaye, 121, 404 et autres nombres palindromes (in French), Pour La Science, 480, October 2017.

EXAMPLE

Triangle begins:

  6643,

     5,  10,

    31,  26, 46,

     7,  28, 21, 67,

    85,   8, 85, 24,  92,

     9, 121, 63, 18, 154, 121,

  ...

MATHEMATICA

palQ[n_Integer, base_Integer] := Block[{}, Reverse[idn = IntegerDigits[n, base]] == idn]; Table[ t[n, k], {n, 3, 13}, {k, 2, n - 1}] // Flatten (* Robert G. Wilson v, Nov 17 2017 *)

PROG

(PARI) isok(j, n, k) = my(dn=digits(j, n), dk=digits(j, k)); (Vecrev(dn)==dn) && (Vecrev(dk)==dk);

T(n, k) = {j = max(n, k); while(! isok(j, n, k), j++); j; }

tabl(nn) = for (n=3, nn, for (k=2, n-1, print1(T(n, k), ", ")); print);

CROSSREFS

Cf. A048268 (right diagonal), A056749 (1st column).

Sequence in context: A345571 A345827 A196510 * A048268 A043634 A060792

Adjacent sequences:  A293922 A293923 A293924 * A293926 A293927 A293928

KEYWORD

nonn,base,tabl

AUTHOR

Michel Marcus, Nov 16 2017

STATUS

approved

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Last modified January 21 15:30 EST 2022. Contains 350479 sequences. (Running on oeis4.)