A372557 Numbers k such that the least number of Jacobsthal numbers that add up to k, A372555(k), is less than the number needed with the greedy algorithm, A265745(k).

63, 84, 148, 169, 191, 212, 234, 255, 276, 297, 319, 340, 404, 425, 489, 510, 532, 553, 575, 596, 617, 638, 660, 681, 703, 724, 746, 767, 788, 809, 831, 852, 874, 895, 917, 937, 938, 959, 980, 1002, 1022, 1023, 1044, 1065, 1087, 1108, 1129, 1150, 1172, 1193, 1215, 1236, 1258, 1278, 1279, 1300, 1321, 1343, 1363, 1364, 1428

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..22785

Example

63 = 21+21+21 has A372555(63)=3 for its optimal, non-greedy solution, and A265745(63) = 5 for its greedy solution 63 = 43+11+5+3+1, therefore 63 is included in this sequence. (From Yuriko Suwa's Jul 11 2021 comment in A265745.)
84 = 21+21+21+21 has A372555(84)=4 for its optimal, non-greedy solution, and A265745(84) = 6 for its greedy solution 84 = 43+21+11+5+3+1, therefore 84 is included in this sequence.
169 = 85+21+21+21+21 has A372555(169)=5 for its optimal, non-greedy solution, and A265745(169) = 7 for its greedy solution 169 = 85+43+21+11+5+3+1, therefore 169 is included in this sequence.

Prog

(PARI)
\\ For A372555, use the program given under that entry.
A130249(n) = (#binary(3*n+1)-1);
A001045(n) = (2^n - (-1)^n) / 3;
A265745(n) = { my(s=0); while(n, s++; n -= A001045(A130249(n))); (s); };
isA372557(k) = (A372555(k)<A265745(k));

Crossrefs

Cf. A001045, A265745, A372555.

Cf. A372558 (subsequence).

Sequence in context: A046049 A240528 A320066 * A372558 A125112 A043186

Adjacent sequences: A372554 A372555 A372556 * A372558 A372559 A372560

Keyword

nonn,changed

Author

Antti Karttunen, May 07 2024

Status

approved