

A131357


a(1) = 1, a(2) = 2; for n > 1, a(n) = sum of the next two smallest integers > a(n1) which are coprime to the sum s = a(1) + ... + a(n1).


2



1, 2, 9, 24, 54, 120, 248, 500, 1004, 2016, 4038, 8082, 16170, 32346, 64700, 129404, 258812, 517644, 1035294, 2070594, 4141194, 8282394, 16564800, 33129608, 66259220, 132518444, 265036896, 530073798, 1060147602, 2120295210, 4240590426, 8481180858, 16962361722, 33924723450, 67849446906, 135698893818
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OFFSET

1,2


LINKS

Michel Marcus, Table of n, a(n) for n = 1..1000


FORMULA

Conjecture: a(n) ~ 2^(n+1) * 0.9873393997556885598467...  Petros Hadjicostas, Jun 23 2019 [Constant evaluated using Michel Marcus's bfile]


EXAMPLE

n = 3: a(1) = 1, a(2) = 2, s = 1 + 2 = 3; n1 = 4 (not 3) and n2 = 5 are both coprime to s, hence a(3) = n1 + n2 = 9;
n = 4: a(1) = 1, a(2) = 2, a(3) = 9, s = 1 + 2 + 9 = 12; n1 = 11 (not 10 or 12) and n2 = 13 are both coprime to s, hence a(4) = n1 + n2 = 24;
n = 5: s = 36; n1 = 25 (not 26, 27, or 28) and n2 = 29 are both coprime to s, hence a(5) = n1 + n2 = 54;
n = 6: s = 90; n1 = 59 (not 55, 56, 57, 58, or 60) and n2 = 61 are both comprime to s, hence a(6) = n1 + n2 = 120.


PROG

(PARI) findnext(last, s) = {my(x = last+1); while (gcd(x, s) != 1, x++); my(y = x+1); while (gcd(y, s) != 1, y++); x+y; }
lista(nn) = {my(v = [1, 2], val); print1(v[1], ", ", v[2], ", "); for (n=3, nn, val = findnext(v[#v], vecsum(v)); v = concat(v, val); print1(val, ", "); ); } \\ Michel Marcus, Jun 25 2019


CROSSREFS

Sequence in context: A006002 A259969 A023662 * A274543 A079997 A275260
Adjacent sequences: A131354 A131355 A131356 * A131358 A131359 A131360


KEYWORD

nonn


AUTHOR

Zak Seidov, Sep 30 2007


EXTENSIONS

More terms from Petros Hadjicostas, Jun 23 2019


STATUS

approved



