A083142 -id:A083142 - cp's OEIS frontend

A329544 Add the odd terms and subtract the even ones, the result must always be a palindrome. This is the lexicographically earliest sequence of distinct positive integers with this property.

1, 3, 2, 5, 4, 19, 11, 22, 6, 17, 14, 8, 7, 15, 16, 27, 24, 13, 18, 29, 26, 37, 33, 44, 28, 39, 36, 25, 30, 41, 38, 49, 46, 35, 40, 51, 48, 59, 45, 10, 68, 32, 21, 20, 9, 55, 58, 47, 50, 61, 60, 71, 66, 77, 23, 12, 88, 191, 101, 111, 91, 112, 31, 81, 121, 131, 141, 70, 132, 80, 122, 90, 142, 174, 43, 54, 72, 83, 53, 42

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Nov 16 2019

Negative palindromes are not allowed (0 is OK). After 50000 terms, the smallest unused integers are 919, 1020, 1029, 1031, 1038, 1041, 1047, ... and the largest used is 208831. The largest palindrome produced so far is 1000001. Is the sequence a permutation of the integers > 0?
After one million terms, the smallest unused integers are still the seven mentioned (above) for 50000 terms. - Hans Havermann, Nov 27 2019
This sequence is not a permutation of the nonnegative integers because it cannot contain any term of A104444. The value 919 may only appear after a running total equal to 0 (see A083142, A084843). - Rémy Sigrist, Dec 11 2019. There are only two 0's in the first million terms of A329796, at n=12 and n=1002, so the chance that this happens seems slight. On the other hand, the zeros in the base 3 analog, A330314, are more plentiful (see A330325), so further investigation is needed. - Hans Havermann and N. J. A. Sloane, Dec 12 2019

			The sequence starts with 1 which is positive and a palindrome.
1 + 3 = 4 (palindrome). (2 is not allowed because 1 - 2 < 0.)
1 + 3 - 2 = 2 (palindrome)
1 + 3 - 2 + 5 = 7 (palindrome)
1 + 3 - 2 + 5 - 4 = 3 (palindrome)
1 + 3 - 2 + 5 - 4 + 19 = 22 (palindrome)
1 + 3 - 2 + 5 - 4 + 19 + 11 = 33 (palindrome)
1 + 3 - 2 + 5 - 4 + 19 + 11 - 22 = 11 (palindrome), etc.

Jean-Marc Falcoz, Table of n, a(n) for n = 1..50000.
Hans Havermann, High-resolution graph of 100000 terms showing even/odd distribution
N. J. A. Sloane, Table of n, a(n), A329796(n), A329796(n)/a(n) for n = 1..50000
N. J. A. Sloane (in collaboration with Scott R. Shannon), Art and Sequences, Slides of guest lecture in Math 640, Rutgers Univ., Feb 8, 2020. Mentions this sequence.

Cf. A329545 (same idea, but where the odd integers are subtracted and the even ones are added).
Cf. A002113 (palindromes), A086862 (first differences), A104444, A329796 (running totals), A329797, A329798 (records), A330311 (when n appears).
See also A083142, A084843, A330313, A330314, A330325.

A329544_vec(N,u=1,U,a,s,d)={vector(N,n, a=u; while(bittest(U,a-u)|| Vecrev(d=digits(s-(-1)^a*a))!=d|| (a>s&&!bittest(a,0)),a++); s-=(-1)^a*a; U+=1<<(a-u); while(bittest(U,0), U>>=1; u++);a)} \\ M. F. Hasler, Nov 16 2019

A213879 Positive palindromes that are not the sum of two positive palindromes.

Original entry on oeis.org

1, 111, 131, 141, 151, 161, 171, 181, 191, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 10301, 10401, 10501, 10601, 10701, 10801, 10901, 11111, 11211, 11311, 11411, 11511, 11611, 11711, 11811, 11911, 12021, 12121, 12321, 12421, 12521, 12621, 12721, 12821

Offset: 1

Arkadiusz Wesolowski, Jun 23 2012

These numbers do not occur in A035137.

			22 is not a member because 22 = 11 + 11.

Alois P. Heinz, Table of n, a(n) for n = 1..2151 (first 111 terms from N. J. A. Sloane)
Eric Weisstein's World of Mathematics, Palindromic Number
Index entries for sequences related to palindromes

Cf. A002113, A014092, A035137, A083142, A088601, A260255, A319477.

# From N. J. A. Sloane, Sep 09 2015: bP is a list of the palindromes
a:={}; M:=400; for n from 3 to M do p:=bP[n];
# is p a sum of two palindromes?
sw:=-1; for i from 2 to n-1 do j:=p-bP[i]; if digrev(j)=j then sw:=1; break; fi;
od;
if sw<0 then a:={op(a),p}; fi; od:
b:=sort(convert(a,list));

lst1 = {}; lst2 = {}; r = 12821; Do[If[FromDigits@Reverse@IntegerDigits[n] == n, AppendTo[lst1, n]], {n, r}]; l = Length[lst1]; Do[s = lst1[[i]] + lst1[[j]]; AppendTo[lst2, s], {i, l - 1}, {j, i}]; Complement[lst1, lst2]
palQ[n_] := Reverse[x = IntegerDigits[n]] == x; t1 = Select[Range[12900], palQ[#] &]; Complement[t1, Union[Flatten[Table[i + j, {i, t1}, {j, t1}]]]] (* Jayanta Basu, Jun 15 2013 *)

({ A002113 } intersect { A319477 }) minus { 0 }. - Alois P. Heinz, Sep 19 2018

cp's OEIS Frontend

A329544 Add the odd terms and subtract the even ones, the result must always be a palindrome. This is the lexicographically earliest sequence of distinct positive integers with this property.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI