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A364214 Numbers whose canonical representation as a sum of distinct Jacobsthal numbers (A280049) is palindromic.

%I A364214 #9 Mar 30 2024 23:07:46
%S A364214 1,2,4,5,6,10,12,15,18,21,22,30,34,42,44,49,58,63,66,71,80,85,86,102,
%T A364214 110,126,130,146,154,170,172,183,198,209,218,229,244,255,258,269,284,
%U A364214 295,304,315,330,341,342,374,390,422,430,462,478,510,514,546,562,594
%N A364214 Numbers whose canonical representation as a sum of distinct Jacobsthal numbers (A280049) is palindromic.
%C A364214 The even-indexed Jacobsthal numbers A001045(2*n) = A002450(n) = (4^n-1)/3, for n >= 1, are terms since their representation is 2*n-1 1's.
%C A364214 A001045(2*n+1) - 1 = A020988(n) = (2/3)*(4^n-1) is a term for n >= 1, since its representation is 2*n 1's.
%C A364214 A001045(n) + 1 = A128209(n) is a term for n >= 0, since its representation for n = 0 is 1 and its representation for n >= 1 is n-1 0's between 2 1's.
%C A364214 A160156(n) is a term for n >= 0 since its representation is n 0's interleaved with n+1 1's.
%H A364214 Amiram Eldar, <a href="/A364214/b364214.txt">Table of n, a(n) for n = 1..10000</a>
%e A364214 The first 10 terms are:
%e A364214    n  a(n)  A280049(a(n))
%e A364214   --  ----  -------------
%e A364214    1     1              1
%e A364214    2     2             11
%e A364214    3     4            101
%e A364214    4     5            111
%e A364214    5     6           1001
%e A364214    6    10           1111
%e A364214    7    12          10001
%e A364214    8    15          10101
%e A364214    9    18          11011
%e A364214   10    21          11111
%t A364214 Position[Select[Range[1000], EvenQ[IntegerExponent[#, 2]] &], _?(PalindromeQ[IntegerDigits[#, 2]] &)] // Flatten
%o A364214 (PARI) s(n) = if(n < 2, n > 0, n = s(n-1); until(valuation(n, 2)%2 == 0, n++); n); \\ A003159
%o A364214 is(n) = {my(d = binary(s(n))); d == Vecrev(d);}
%Y A364214 Cf. A001045, A002450, A003159, A020988, A280049.
%Y A364214 Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087, A352105, A352319, A352341.
%K A364214 nonn,base,easy
%O A364214 1,2
%A A364214 _Amiram Eldar_, Jul 14 2023