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

1, 2, 4, 5, 6, 10, 12, 15, 18, 21, 22, 30, 34, 42, 44, 49, 58, 63, 66, 71, 80, 85, 86, 102, 110, 126, 130, 146, 154, 170, 172, 183, 198, 209, 218, 229, 244, 255, 258, 269, 284, 295, 304, 315, 330, 341, 342, 374, 390, 422, 430, 462, 478, 510, 514, 546, 562, 594

Offset

1,2

Comments

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.

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.

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.

A160156(n) is a term for n >= 0 since its representation is n 0's interleaved with n+1 1's.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The first 10 terms are:
   n  a(n)  A280049(a(n))
  --  ----  -------------
   1     1              1
   2     2             11
   3     4            101
   4     5            111
   5     6           1001
   6    10           1111
   7    12          10001
   8    15          10101
   9    18          11011
  10    21          11111

Mathematica

Position[Select[Range[1000], EvenQ[IntegerExponent[#, 2]] &], _?(PalindromeQ[IntegerDigits[#, 2]] &)] // Flatten

Prog

(PARI) s(n) = if(n < 2, n > 0, n = s(n-1); until(valuation(n, 2)%2 == 0, n++); n); \\ A003159
is(n) = {my(d = binary(s(n))); d == Vecrev(d); }

Crossrefs

Cf. A001045, A002450, A003159, A020988, A280049.

Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087, A352105, A352319, A352341.

Sequence in context: A061949 A233413 A128167 * A162534 A233193 A177911

Adjacent sequences: A364211 A364212 A364213 * A364215 A364216 A364217

Keyword

nonn,base,easy

Author

Amiram Eldar, Jul 14 2023

Status

approved