

A004978


a(n) = least integer m > a(n1) such that m  a(n1) != a(j)  a(k) for all j, k less than n; a(1) = 1, a(2) = 2.
(Formerly N0416)


10



1, 2, 4, 8, 13, 21, 31, 45, 60, 76, 97, 119, 144, 170, 198, 231, 265, 300, 336, 374, 414, 456, 502, 550, 599, 649, 702, 759, 819, 881, 945, 1010, 1080, 1157, 1237, 1318, 1401, 1486, 1572, 1662, 1753, 1845, 1945, 2049, 2156, 2264
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OFFSET

1,2


COMMENTS

Equivalently, if S(n) = { a(j)  a(k); n > j > k > 0 }, then a(n) = a(n1) + M where M = min( {1, 2, 3, ...} \ S(n) ) is the smallest positive integer not in S(n).  M. F. Hasler, Jun 26 2019


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).


LINKS



EXAMPLE

After a(1) = 1, a(2) = 2, we have a(3) = least m > a(2) such that m  a(2) = m  2 is not in { a(j)  a(k); 1 <= k < j < 3 } = { a(2)  a(1) } = { 1 }. Thus we must have m  2 = 2, whence m = 4.
The next term a(4) is the least m > a(3) such that m  a(3) = m  4 is not in { a(j)  a(k); 1 <= k < j < 4 } = { 1, 4  2 = 2, 4  1 = 3 }, i.e., m = 4 + 4 = 8.
The next term a(5) is the least m > a(4) such that m  a(4) = m  8 is not in { a(j)  a(k); 1 <= k < j < 5 } = { 1, 2, 3, 8  4 = 4, 8  2 = 6, 8  1 = 7 }, i.e., m = 5 + 8 = 13.
(End)


PROG

for n=3:2000
d=sort(unique(d));
end
(PARI) A004978_vec(N, a=[1..N], S=[1])={for(n=3, N, a[n]=a[n1]+S[1]+1; S=setunion(S, select(t>t>S[1], vector(n1, k, a[n]a[nk]))); for(k=1, #S1, if(S[k+1]S[k]>1, S=S[k..1]; next(2))); S[#S]==#S&&S=[#S]); a} \\ M. F. Hasler, Jun 26 2019


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

Definition corrected by Bryan S. Robinson, Mar 16 2006


STATUS

approved



