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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)).
2
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
1,2
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
LINKS
Eric Angelini, Échecs et Maths, Personal blog, bottom of the page, July 2023.
Hans Havermann, 100000 terms, July 2023
EXAMPLE
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
PROG
(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
CROSSREFS
Cf. A300000.
Sequence in context: A299952 A278672 A129542 * A224752 A224761 A171315
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Hans Havermann, Jul 03 2023
STATUS
approved