# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a359482 Showing 1-1 of 1 %I A359482 #45 Aug 02 2023 11:50:50 %S A359482 1,10,99,889,8009,1101,9089,80718,100284,183899,206021,396118,215703, %T A359482 354632,108578,469891,229021,61195,34146,7321,13817,3536,1825,749,167, %U A359482 508,324,2096,4337,2958,2870,4171,12941,16470,30560,25465,21056,35296,17665,35927,23345,10106,548,279,516,1094,3228,5302 %N 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)). %C A359482 Is this sequence a permutation of the integers > 0? %C A359482 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 %H A359482 Eric Angelini, Échecs et Maths, Personal blog, bottom of the page, July 2023. %H A359482 Hans Havermann, 100000 terms, July 2023 %e A359482 1 + 10 = 11 and 11 is a substring of concat(1, 10) = 110. %e A359482 10 + 99 = 109 and 109 is a substring of concat(10, 99) = 1099. %e A359482 99 + 889 = 988 and 988 is a substring of concat(99, 889) = 99889. %e A359482 889 + 8009 = 8898 and 8898 is a substring of 8898009. %e A359482 8009 + 1101 = 9110 and 9110 is a substring of 80091101, etc. %e A359482 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 %o A359482 (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 %Y A359482 Cf. A300000. %K A359482 base,nonn %O A359482 1,2 %A A359482 _Eric Angelini_ and _Hans Havermann_, Jul 03 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE