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 A328861 Concatenation of the permutation of (1, ..., n) that maximizes the minimal sum of increasing concatenations. 2
 1, 21, 132, 4321, 43521, 154632, 6517432, 76518432, 768519432, 98471106532, 1651142910873, 411129101287653, 97864125313121110, 4211113109141287653 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the concatenation concat(p_1, ..., p_n) of the smallest permutation p of (1, ..., n) such that M(p) = min {S(v); v in C(p)} is maximal, where S(v) is the sum of v's components, and C(p) is the set of all vectors v with increasing components (v_1 < ... < v_k) obtained from p by concatenating some or all adjacent components, for example v = (concat(p_1, p_2), p_3, concat(p_4, ..., p_n)). Terms were computed by Frank Stevenson, for n < 10 double-checked with given PARI code. LINKS Table of n, a(n) for n=1..14. E. Angelini, Chunk and sum, personal blog "Cinquante Signes", Oct. 2019 EXAMPLE For n = 1, there is only one permutation, p = (1), whence a(1) = 1. For n = 2, the permutation p = (1,2) yields C(p) = {(1,2), (12)} with M(p) = min {1+2, 12} = 3, while p = (2,1) yields C(p) = {(21)} with M(p) = 21, whence a(n) = concat(2,1) = 21. For n = 3, the permutation p = (1,3,2) yields C(p) = {(1,32), (132)} with M(p) = 1+32 = 33, and no other permutation yields a larger minimum. (The permutation (2,3,1) would yield the same minimum but comes later.) Therefore a(3) = 132. a(4) = 4321 with M((4,3,2,1)) = 4+321 = 325. a(5) = 43521 with M((4,3,5,2,1)) = 43+521 = 564. a(6) = 154632 with M((1,5,4,6,3,2)) = 1+54+632 = 687. a(7) = 6517432 with M((6,5,1,7,4,3,2) = 6+51+7432 = 7489. a(8) = 76518432 with M(p) = 7+651+8432 = 9090. a(9) = 768519432 with M(p) = 76+851+9432 = 10359 a(10) = 98471106532 with M(p) = 98+471+106532 = 107101. a(11) = 1651142910873 with M(p) = 1+65+1142+910873 = 912081. a(12) = 411129101287653 with M(p) = 41+112+910+1287653 = 1288716. a(13) = 97864125313121110 with M(p) = 97+864+1253+13121110 = 13123324. a(14) = 4211113109141287653 with M((4,2,1,11,13,10,9,14,12,8,7,6,5,3)) = 42+111+13109+141287653 = 141300915 PROG (PARI) A328861(n, p=0, m)={ if(!p, (p===0&&n>1)||return(n); my(P); forperm(n, p, m<(m=max(A328861(p[1], Vec(p[^1])), m)) && P=p); fromdigits(Vec(P)), n>=m=fromdigits(p), n*10^#p+m, my(s=A328861(n*10+p[1], p[^1]), t); for(k=logint(n, 10)+1, (#p)\2, n<(t=m\10^(#p-k)) && t

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Last modified May 29 18:27 EDT 2023. Contains 363042 sequences. (Running on oeis4.)