A049476 Positions of records in A346778.
1, 2, 5, 13, 14, 26, 61, 63, 111, 131, 151, 153, 155, 161, 179, 295, 390, 391, 398, 425, 428, 459, 485, 656, 675, 1142, 1143, 1169, 1243, 1247, 1255, 1263, 1267, 1639, 1643, 1646, 1748, 2690, 2702, 2703, 2728, 2767, 2777, 2786, 2840, 2877
Offset: 1
Examples
For n = 4, when we examine row 13 in A088643, the Roche algorithm produces the initial row values 13, 10, 9, 8, 11, 12. The remaining values are equal to row 7 in A088643, and at no earlier point in row 13 are the remaining values equal to row m, 7 < m < 13. So we calculate the difference between 13 and 7 ("the uncharted length") to be 6, which is longer than the previous record uncharted length (A049478(3) = 4) set by row a(3) = 5. So a(4) = 13. - _Peter Munn_, Aug 03 2021 (based on text supplied by _J. Stauduhar_)
Links
- J. W. Roche, Letter regarding "M. J. Kenney and S. J. Bezuszka, Calendar problem 12, 1997", Mathematics Teacher, 91 (1998), 155.
Programs
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PARI
{print1(m=0); for( n=1, oo, my( r=A088643_row(n)); for( g=1, #r-1, if( Set(r[1..g]) == [n-g+1..n] && r[g+1]==n-g, g > m && print1(","n)+ m=g; break)))} \\ M. F. Hasler, Aug 04 2021
Extensions
Revised by Sean A. Irvine, Aug 03 2021
Comments