Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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