A359482 Lexicographically earliest sequence of distinct terms > 0 such that the sum a(n) + a(n+1) is a substring of the concatenation (a(n), a(n+1)).

1, 10, 99, 889, 8009, 1101, 9089, 80718, 100284, 183899, 206021, 396118, 215703, 354632, 108578, 469891, 229021, 61195, 34146, 7321, 13817, 3536, 1825, 749, 167, 508, 324, 2096, 4337, 2958, 2870, 4171, 12941, 16470, 30560, 25465, 21056, 35296, 17665, 35927, 23345, 10106, 548, 279, 516, 1094, 3228, 5302

Offset: 1

Author

Eric Angelini and Hans Havermann, Jul 03 2023

Keywords

• base
• nonn

Comments

Is this sequence a permutation of the integers > 0?

I conjecture that it isn't, and more specifically, that a(1) = 1 is the only single-digit term, and a(2) = 10 the only multiple of 10 below 100. See Examples for other terms of the form x*10^k, 1 <= x <= 9. - M. F. Hasler, Jul 03 2023

Examples

			1 + 10 = 11 and 11 is a substring of concat(1, 10) = 110.
10 + 99 = 109 and 109 is a substring of concat(10, 99) = 1099.
99 + 889 = 988 and 988 is a substring of concat(99, 889) = 99889.
889 + 8009 = 8898 and 8898 is a substring of 8898009.
8009 + 1101 = 9110 and 9110 is a substring of 80091101, etc.
Some examples of terms of the form x*10^k, x < 10: a(2136) = 800, a(4204) = 1000, a(6246) = 900, a(6618) = 100, a(11268) = 400, a(17446) = 10000, a(39292) = 600, a(44989) = 700, a(91359) = 300, ... - _M. F. Hasler_, Jul 03 2023
		

Links

• Eric Angelini, Échecs et Maths, Personal blog, bottom of the page, July 2023.
• Hans Havermann, 100000 terms, July 2023

Crossrefs

Cf. A300000.

Programs

PARI

A359482_first(n)={my(ok(a,k)=my(c=a*10^logint(k*10,10)+k); k=10^logint(10*a+=k,10); until(a>c\=10, c%k==a&& return(1)), U=[], a=0); vector(n,n, my(k=1); while(setsearch(U,k)|| !ok(a,k), k++); U=setunion(U,[k]); a=k)} \\ Becomes slow for n > 10. - M. F. Hasler, Jul 03 2023