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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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)

Paul Tek, PERL program for this sequence

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

CROSSREFS

Cf. A002113, A055266.

Cf. A062932 (strictly increasing variant).

Sequence in context: A171610 A004835 A037341 * A062932 A166098 A124365

Adjacent sequences:  A228727 A228728 A228729 * A228731 A228732 A228733

KEYWORD

nonn,base

AUTHOR

Paul Tek, Aug 31 2013

EXTENSIONS

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

STATUS

approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)