

A299952


The sum a(n) + a(n+1) is a substring of the concatenation of all terms up to a(n+1). Lexicographic first sequence of positive integers without duplicate terms having this property.


2



1, 10, 99, 11, 80, 19, 61, 30, 31, 49, 12, 2, 4, 5, 3, 6, 7, 15, 9, 13, 17, 14, 8, 16, 20, 25, 23, 22, 26, 27, 18, 34, 28, 21, 24, 29, 32, 35, 36, 44, 37, 43, 38, 33, 41, 39, 42, 40, 51, 45, 46, 47, 52, 57, 53, 56, 54, 55, 63, 59, 50, 60, 58, 64, 66, 65, 74, 48, 62, 68, 71, 77, 72, 67, 78, 70
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OFFSET

1,2


COMMENTS

The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that does not lead to a contradiction.
This is probably a permutation of the natural numbers (after 10000 terms, the smallest integer not yet present is 9990).


LINKS

Lars Blomberg, Table of n, a(n) for n = 1..10000


EXAMPLE

a(1) + a(2) = 1 + 10 = 11 and “11” is visible in [1,10]
a(2) + a(3) = 10 + 99 = 109 and “109” is visible in [10,99]
a(3) + a(4) = 99 + 11 = 110 and “110” is visible in [1,10]
a(4) + a(5) = 11 + 80 = 91 and “91” is visible in [99,11]
a(5) + a(6) = 80 + 19 = 99 and “99” is visible in [99]
a(6) + a(7) = 19 + 61 = 80 and “80” is visible in [80]
...


MATHEMATICA

Nest[Function[a, Append[a, Block[{k = 1, d}, While[Nand[FreeQ[a, k], SequenceCount[Flatten@ IntegerDigits[Append[a, k]], IntegerDigits[a[[1]] + k]] > 0], k++]; k]]], {1}, 75] (* Michael De Vlieger, Feb 22 2018 *)


PROG

(PARI) a(n, show=1, a=1, s=a, u=[a], t, m)={for(n=2, n, show&&print1(a", "); for(k=u[1]+1, oo, setsearch(u, k)&&next; m=Mod(a+k, 10^#Str(a+k)); t=s*10^#Str(k)+k; until(k>=t\=10, t==m&&(a=k)&&break(2))); s=s*10^#Str(a)+a; u=setunion(u, [a]); u[2]==u[1]+1&&u=u[^1]); a} \\ M. F. Hasler, Feb 22 2018


CROSSREFS

Cf. A300000.
For a different constraint on a(n)+a(n+1) (must have a digit '1'), see A299957 and A299970, A299982, ..., A299988, A299969 (nonnegative analog with digit 0, 2, ..., 9), A299971, A299972, ..., A299979 (positive analog with digit 0, 2, ..., 9).
Cf. A299980, A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979 for the analog using multiplication: a(n)*a(n+1) has a digit 0, resp. 1, ..., resp. 9.
Sequence in context: A217634 A007137 A135927 * A278672 A129542 A224752
Adjacent sequences: A299949 A299950 A299951 * A299953 A299954 A299955


KEYWORD

nonn,base


AUTHOR

Eric Angelini and Lars Blomberg, Feb 22 2018


STATUS

approved



