

A228730


Lexicographically earliest sequence of distinct nonnegative integers such that the sum of two consecutive terms is a palindrome in base 10.


12



0, 1, 2, 3, 4, 5, 6, 16, 17, 27, 28, 38, 39, 49, 50, 51, 15, 7, 26, 18, 37, 29, 48, 40, 59, 42, 13, 9, 24, 20, 35, 31, 46, 53, 58, 8, 14, 19, 25, 30, 36, 41, 47, 52, 69, 32, 12, 10, 23, 21, 34, 43, 45, 54, 57, 44, 11, 22, 33, 55, 56, 65, 66, 75, 76, 85, 86, 95, 96
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OFFSET

0,3


COMMENTS

At each step, choose the smallest number not occurring earlier and such that a(n+1)+a(n) are palindromes, for all n.
Conjectured to be a permutation of the nonnegative integers.
See A062932 where injectivity is replaced by monotonicity; the sequences differ from a(16)=15 on.
This is an "arithmetic" analog to sequences A228407 and A228410, where instead of the sum, the union of the digits of subsequent terms is considered. (End)


LINKS



EXAMPLE

a(1) + a(2) = 3.
a(2) + a(3) = 5.
a(3) + a(4) = 7.
a(4) + a(5) = 9.
a(5) + a(6) = 11.
a(6) + a(7) = 22.
a(7) + a(8) = 33.


PROG

(Perl) See Link section.
(PARI) {a=0; u=0; for(n=1, 99, u+=1<<a; print1(a", "); for(k=1, 9e9, !bittest(u, k)&&is_A002113(a+k)&&(a=k)&&next(2)))} \\ M. F. Hasler, Nov 09 2013
(Python)
from itertools import islice
def ispal(n): s = str(n); return s == s[::1]
def agen(): # generator of terms
aset, an, mink = {0}, 0, 1
yield 0
while True:
k = mink
while k in aset or not ispal(an + k): k += 1
an = k; aset.add(an); yield an
while mink in aset: mink += 1


CROSSREFS

Cf. A062932 (strictly increasing variant).


KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



