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

1,2

Comments

Previous name: Row numbers that set records for initial gap lengths g in the permutations found in A088643.

Links

Table of n, a(n) for n=1..46.

J. W. Roche, Letter regarding "M. J. Kenney and S. J. Bezuszka, Calendar problem 12, 1997", Mathematics Teacher, 91 (1998), 155.

Example

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)

Prog

(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

Crossrefs

Cf. A049477, A049478, A088643, A346778.

Sequence in context: A127987 A247543 A220268 * A216889 A334494 A168486

Adjacent sequences: A049473 A049474 A049475 * A049477 A049478 A049479

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Revised by Sean A. Irvine, Aug 03 2021

Status

approved