A133514 Biquadrateful (i.e., not biquadrate-free) palindromes.

272, 464, 656, 848, 2112, 2992, 4224, 6336, 8448, 14641, 21312, 21712, 23232, 23632, 25152, 25552, 25952, 27072, 27472, 27872, 29392, 29792, 31213, 40304, 40704, 42224, 42624, 44144, 44544, 44944, 46064, 46464, 46864, 48384, 48784, 61216, 61616, 62426, 63136

Offset

1,1

Comments

This is to A035133 as 4th powers are to cubes. To make an analogy between analogies, the preceding sentence is to "A130873 is to 4th powers as A120398 is to cubes" as palindromes are to sums of two distinct prime powers.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

A002113 INTERSECTION A046101.

Example

a(10) = 14641 = 11^4 (the smallest odd value in this sequence).
a(11) = 21312 = 2^6 * 3^2 * 37.

Maple

isA046101 := proc(n) local ifs, f ; ifs := ifactors(n)[2] ; for f in ifs do if op(2, f) >= 4 then RETURN(true) ; fi ; od: RETURN(false) ; end: isA002113 := proc(n) local digs, i ; digs := convert(n, base, 10) ; for i from 1 to nops(digs) do if op(i, digs) <> op(-i, digs) then RETURN(false) ; fi ; od: RETURN(true) ; end: isA133514 := proc(n) isA046101(n) and isA002113(n) ; end: for n from 1 to 100000 do if isA133514(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, Jan 12 2008
# second Maple program:
q:= n->StringTools[IsPalindrome](""||n) and max(map(i->i[2], ifactors(n)[2]))>3:
select(q, [$1..70000])[];  # Alois P. Heinz, Sep 27 2023

Mathematica

a = {}; For[n = 2, n < 100000, n++, If[FromDigits[Reverse[IntegerDigits[n]]] == n, b = 0; For[l = 1, l < Length[FactorInteger[n]] + 1, l++, If[FactorInteger[n][[l, 2]] > 3, b = 1]]; If[b == 1, AppendTo[a, n]]]]; a (* Stefan Steinerberger, Dec 26 2007 *)
Select[Range@100000, PalindromeQ@#&&3<Max@Last@Transpose@FactorInteger@#&] (* Hans Rudolf Widmer, Sep 27 2023 *)

Crossrefs

Cf. A002113, A046101.

Sequence in context: A316574 A062906 A253361 * A235293 A270302 A304549

Adjacent sequences: A133511 A133512 A133513 * A133515 A133516 A133517

Keyword

base,nonn

Author

Jonathan Vos Post, Nov 30 2007

Extensions

More terms from Stefan Steinerberger, Dec 26 2007

More terms from R. J. Mathar, Jan 12 2008

Status

approved