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%I #40 Aug 08 2021 03:50:21
%S 1,2,5,13,14,26,61,63,111,131,151,153,155,161,179,295,390,391,398,425,
%T 428,459,485,656,675,1142,1143,1169,1243,1247,1255,1263,1267,1639,
%U 1643,1646,1748,2690,2702,2703,2728,2767,2777,2786,2840,2877
%N Positions of records in A346778.
%C Previous name: Row numbers that set records for initial gap lengths g in the permutations found in A088643.
%H J. W. Roche, <a href="http://www.jstor.org/stable/27970468">Letter regarding "M. J. Kenney and S. J. Bezuszka, Calendar problem 12, 1997"</a>, Mathematics Teacher, 91 (1998), 155.
%e 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_)
%o (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
%Y Cf. A049477, A049478, A088643, A346778.
%K nonn,nice
%O 1,2
%A _N. J. A. Sloane_
%E Revised by _Sean A. Irvine_, Aug 03 2021
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