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A268132 If a(n) is a square (and n > 1), then a(n+1) = a(n) + a(n-1), 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 (list; graph; refs; listen; history; text; internal format)
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(n-1) and equal to an earlier term a(m+1) of the same form, where furthermore the predecessor a(m-1) 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[#a-1]))); 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

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Last modified October 16 15:31 EDT 2019. Contains 328101 sequences. (Running on oeis4.)