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, 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

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