A228730 Lexicographically earliest sequence of distinct nonnegative integers such that the sum of two consecutive terms is a palindrome in base 10.

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

Author

Paul Tek, Aug 31 2013

Keywords

• nonn
• base

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)

Examples

			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.
		

Links

• Paul Tek, Table of n, a(n) for n = 0..10000 (corrected by Michel Marcus, Jan 19 2019)
• Paul Tek, PERL program for this sequence

Crossrefs

Cf. A002113, A055266.

Cf. A062932 (strictly increasing variant).

Programs

PARI

{a=0;u=0; for(n=1, 99, u+=1<A002113(a+k)&&(a=k)&&next(2)))} \\ M. F. Hasler, Nov 09 2013

Perl

See Link section.

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

Extensions

a(0)=0 added by M. F. Hasler, Nov 15 2013