

A268132


If a(n) is a square (and n > 1), then a(n+1) = a(n) + a(n1), else a(n+1) is the smallest positive integer not occurring earlier.


1



1, 2, 3, 4, 7, 5, 6, 8, 9, 17, 10, 11, 12, 13, 14, 15, 16, 31, 18, 19, 20, 21, 22, 23, 24, 25, 49, 74, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 71, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 127, 65, 66, 67, 68, 69, 70, 72, 73, 75, 76, 77, 78, 79, 80, 81, 161
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OFFSET

1,2


COMMENTS

A variant of the sequence A267758 where the relation has to hold for prime numbers rather than for squares.
Conjectured to be a permutation of the positive integers (which could be enforced by definition). In case there would occur a duplicate, it must be of the form a(n+1) = a(n) + a(n1) and equal to an earlier term a(m+1) of the same form, where furthermore the predecessor a(m1) also is of that form, since otherwise a(m+1) would be smaller than this a(n+1). This seems extremely unlikely to happen, and maybe provably impossible.


LINKS

M. F. Hasler, Table of n, a(n) for n = 1..1000


EXAMPLE

a(26) = 25 is a square, thus followed by a(26) + a(25) = 25 + 24 = 49 which is again a square, thus followed by 49 + 25 = 74. Where is the next occurrence of two subsequent squares?


PROG

(PARI) a(n, show=0, is=x>issquare(x), a=[1], L=0, U=[])={while(#a<n, show&&if(type(show)=="t_STR", write(show, #a, " ", a[#a]), print1(a[#a]", ")); if(a[#a]>L+1, U=setunion(U, [a[#a]]), L++; while(#U&&U[1]<=L+1, U=U[^1]; L++)); a=concat(a, if(!is(a[#a])#a<2, L+1, a[#a]+a[#a1]))); if(type(show)=="t_VEC", a, a[#a])}


CROSSREFS

Sequence in context: A073195 A073199 A125988 * A085160 A086429 A085172
Adjacent sequences: A268129 A268130 A268131 * A268133 A268134 A268135


KEYWORD

nonn


AUTHOR

M. F. Hasler, Jan 26 2016


STATUS

approved



