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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
OFFSET
0,3
COMMENTS
From M. F. Hasler, Nov 09 2013: (Start)
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
Paul Tek, Table of n, a(n) for n = 0..10000 (corrected by Michel Marcus, Jan 19 2019)
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
print(list(islice(agen(), 70))) # Michael S. Branicky, Nov 07 2022
CROSSREFS
Cf. A062932 (strictly increasing variant).
Sequence in context: A171610 A004835 A037341 * A062932 A347167 A166098
KEYWORD
nonn,base
AUTHOR
Paul Tek, Aug 31 2013
EXTENSIONS
a(0)=0 added by M. F. Hasler, Nov 15 2013
STATUS
approved