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

Author

Jonathan Vos Post, Nov 30 2007

Keywords

• base
• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A002113, A046101.

Programs

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@#&&3Hans Rudolf Widmer, Sep 27 2023 *)

Formula

A002113 INTERSECTION A046101.

Extensions

More terms from Stefan Steinerberger, Dec 26 2007

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