

A358793


Lexicographically earliest sequence of positive and unique integers such that 2*Sum_{k = 1..n} a(k) = Sum_{k = 1..n} a(a(k)) for n > 1 and a(1) = 1.


0



1, 3, 7, 5, 10, 8, 14, 16, 11, 20, 22, 13, 26, 28, 17, 32, 34, 19, 38, 40, 23, 44, 46, 25, 50, 52, 29, 56, 58, 31, 62, 64, 35, 68, 70, 37, 74, 76, 41, 80, 82, 43, 86, 88, 47, 92, 94, 49, 98, 100, 53, 104, 106, 55, 110, 112, 59, 116, 118, 61, 122, 124, 65, 128
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OFFSET

1,2


COMMENTS

There is a second version of this sequence possible if we change the definition to a(1) = 2 and a(n) > 1, then the sequence will start 2, 4, 5, 8, 10, 7, 14, ... . It will after this continue in the same way as our actual sequence does (and would also extend the valid range of the recurrence formulas).
Start a(1) = 2 and value 1 allowed is A257794.


LINKS



FORMULA

G.f.: x*(1 + 3*x + 7*x^2 + 4*x^3 + 7*x^4 + x^5 + 8*x^6 + 3*x^7  4*x^8 + 2*x^9  x^10 + x^11  3*x^12 + x^14)/(1  x^3  x^6 + x^9).
a(n) = a(n3) + a(n6)  a(n9) for n >= 16.
a((3*(2*n1)  (1)^n)/4) = (3*(2*n1)  (1)^n)/2, for n > 3.
a(6*n) = 6*n+1, for n > 1.
a(6*n+3) = 6*n+5, for n > 0.
a(n) = 30*n  2*a(n1)  3*a(n2)  3*a(n3)  3*a(n4)  3*a(n5)  2*a(n6)  a(n7)  96, for n > 13.


PROG

(PARI) a(n) = {my(v = [1, 3, 7, 5, 10, 8]); if(n < 7, v[n], n*(1+min(1, n%3))+(n%3 == 0)+(n%6 == 3))}


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



