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A267760
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a(n+1) contains as substring the sum of its first digit plus the last digit of a(n); lexicographic first permutation of the nonnegative integers with this property.
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6
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0, 1, 12, 13, 14, 15, 16, 17, 18, 19, 10, 2, 24, 26, 28, 109, 100, 3, 25, 27, 29, 101, 23, 36, 39, 102, 35, 38, 119, 103, 47, 108, 129, 104, 37, 118, 139, 105, 49, 106, 107, 128, 149, 110, 4, 48, 159, 211, 34, 59, 312, 46, 117, 138, 169, 413, 58, 179, 514, 115, 116, 127, 148, 189, 615, 126, 137, 158, 190, 5, 136, 147, 168, 191, 45, 146, 157, 178, 192, 57, 180, 6, 167, 181, 56, 170, 7
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OFFSET
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0,3
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COMMENTS
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When a(n) is a multiple of 10, then a(n+1) is the least number not occurring earlier. Therefore all nonnegative integers occur.
Numbers starting with and/or having only large digits occur late, typically after numbers ending in zero. This is the case for 1, 2, 3, 4, 5, 6, 7, 8 = a(104), 9 = a(114), ..., 90 = a(647), ..., 98 = a(729), 99 = a(732), ..., respectively preceded by 0, 10, 100, 110, 190, 180, 170, ..., 510, ..., 1310, 1410, ...
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LINKS
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PROG
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(PARI) A267760(n, flag=0, a=List(0), u=[])={ for(n=1, n, u=setunion(u, [a[n]]); if(a[n]==u[#u], bittest(flag, 1) && print1(a[n]", "); bittest(flag, 2) && print1(n-1", ")); if(a[n]==u[1]+1, bittest(flag, 3) && print1(a[n]", "); bittest(flag, 4) && print1(n-1, ", ")); while(#u>1&&u[2]==u[1]+1, u=u[^1]); for(k=u[1]+1, 9e9, setsearch(u, k) && next; d=digits(k); setsearch(Set(if(a[n]%10+d[1]<10, d, vector(#d-1, i, d[i+1]+d[i]*10))), a[n]%10+d[1]) && listput(a, k) && break)); if(bittest(flag, 0), Vec(a), a[n])} \\ flag may be the sum of any of the following: 1: return [a(0)..a(n)], 2: print records, 4: print indices of records, 8: print "late birds" A267771, 16: print indices of late birds.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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