A075560 a(1) = 1, a(n) is the smallest number greater than the previous term that cannot be obtained as the sum of products of any group of earlier terms.

1, 2, 4, 10, 22, 50, 106, 230, 480, 1054, 2656, 6782, 17254, 64366, 212752, 1873528, 9518730

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Example

a(5) = 22, as using 1, 2, 4 and 10 the following numbers can be generated: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 40, 41, 42, 43, 80 and 81. E.g., 19 = 10 + 2*4 + 1.

Prog

(PARI) canMake(n, v) = local(l, newV, m, c, count, mm, x); if (n < 0, return(0)); if (n == 0, return(1)); l = length(v); if (l == 0, return(0)); newV = vector(l - 1, i, v[i]); if (canMake(n, newV), return(1)); m = v[l]; c = l - 1; if (canMake(n - m, newV), return(1)); while (c && v[c]*m > n, c--); for (i = 1, 2^c - 1, count = 0; mm = m; x = i; for (j = 1, c, if (x%2, mm *= v[j], count++; newV[count] = v[j]); x \= 2); for (j = c + 1, l - 1, newV[j - c + count] = v[j]); if (canMake (n - mm, vector(l - 1 - c + count, q, newV[q])), return(1))); 0;
my(v = [2], n = 4); while (1, if (canMake(n, v), n += 2, l = length(v); newV = vector(l + 1); for (i = 1, l, newV[i] = v[i]); newV[l + 1] = n; v = newV; print1(n, ", "); n = 2*n + 2)); \\ David Wasserman, Jan 20 2005

Crossrefs

Sequence in context: A260916 A192627 A275445 * A078040 A240041 A164990

Adjacent sequences: A075557 A075558 A075559 * A075561 A075562 A075563

Keyword

nonn,hard,more

Author

Amarnath Murthy, Sep 24 2002

Extensions

Corrected and extended by David Wasserman, Jan 20 2005

Offset corrected by Mohammed Yaseen, Jul 21 2023

a(14)-a(17) from Jinyuan Wang, Jul 26 2025

Status

approved