

A238948


Start T with a(1)=1 and a(2)=2. We try to set a(n) to be the sum s of the last two decimal digits of T, except that if s is already in the sequence, we replace s with the smallest unused integer that ends with the same digit as s.


1



1, 2, 3, 5, 8, 13, 4, 7, 11, 12, 23, 15, 6, 111, 22, 14, 25, 17, 18, 9, 117, 28, 10, 21, 33, 16, 27, 19, 110, 31, 24, 26, 38, 211, 32, 35, 48, 112, 43, 37, 210, 41, 45, 29, 311, 42, 36, 39, 212, 53, 58, 113, 34, 47, 411, 52, 57, 312, 63, 49, 213, 44, 68, 114, 55, 310, 51, 46, 410, 61, 67, 313, 54, 59, 214, 65, 511, 62, 78, 115, 56, 611, 72, 69, 215, 66, 412, 73, 510, 71, 88, 116, 77, 314, 75, 512, 83, 711, 82, 610, 81, 79, 216, 87, 315, 76, 413
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OFFSET

1,2


COMMENTS

This is not a permutation of the natural numbers; for instance, 100 (or any number ending in "100") does not appear in this sequence since the last two digits of S will never sum to 0, 00, or 100.  Jim Nastos, Mar 13 2014


LINKS

Table of n, a(n) for n=1..107.
E. Angelini, The sum rhymes [Cached copy, with permission]


EXAMPLE

a(3) = 1+2 = 3;
a(4) = 2+3 = 5;
a(5) = 3+5 = 8;
a(6) = 5+8 = 13;
a(7) = 1+3 = 4;
a(8) = 3+4 = 7;
a(9) = 4+7 = 11;
a(10) = 12 because 1+1 = 2 is already in the sequence (as a(2)), and 12 is the smallest unused integer ending with "2";
a(11) = 23 because both 1+2 = 3 and 13 are already in the sequence (as a(3) and a(6), respectively);
a(12) = 15 because 2+3 = 5 is a(5);
a(13) = 1+5 = 6.


CROSSREFS

Sequence in context: A214156 A078414 A254056 * A336716 A345097 A050416
Adjacent sequences: A238945 A238946 A238947 * A238949 A238950 A238951


KEYWORD

nonn,base


AUTHOR

Eric Angelini, Mar 14 2014


STATUS

approved



