A248639 -id:A248639

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A248641

Lexicographically earliest positive sequence which does not contain a 4-term equidistant subsequence (a(n+k*d); k=0,1,2,3) in arithmetic progression.

+10
3

1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 2, 1, 2, 2, 2, 3, 3, 3, 1, 1, 3, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 3, 3, 2, 3, 2, 3, 3, 5, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 2, 2, 2, 3, 1, 2, 1, 1, 1, 2, 2, 2, 3, 4, 2, 3, 2, 2, 2, 3, 3, 1, 3, 3, 3, 5, 5, 4, 1, 1, 1, 3, 1, 2, 3, 1, 5, 3, 2, 6, 1, 3, 2, 2, 3, 2, 1, 1, 3, 3, 1, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

See A248625 for more information, links and examples.

It is a variation of A229037 where 3-term is replaced by 4-term (and with “lead index” 0 instead of 1)

LINKS

Sébastien Palcoux, Table of n, a(n) for n = 0..10000

PROG

(PARI) a=[]; for(n=1, 190, a=concat(a, 1); while(hasAP(a, 4), a[#a]++)); a \\ See A248625 for hasAP().

(SageMath)

cpdef FourFree(int n):

cdef int i, r, k, s, L1, L2, L3

cdef list L, Lb

cdef set b

L=[1, 1, 1]

for k in range(3, n):

b=set()

for i in range(k):

if 3*((k-i)/3)==k-i:

r=(k-i)/3

L1, L2, L3=L[i], L[i+r], L[i+2*r]

s=3*(L2-L1)+L1

if s>0 and L3==2*(L2-L1)+L1:

b.add(s)

if 1 not in b:

L.append(1)

else:

Lb=list(b)

Lb.sort()

for t in Lb:

if t+1 not in b:

L.append(t+1)

break

return L

# Sébastien Palcoux, Aug 28 2019

CROSSREFS

Cf. A248625, A248639, A248640, A248627, A229037, A241752.

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Oct 10 2014

STATUS

approved

A248640

Least nonnegative sequence which does not contain a 5-term equidistant subsequence (a(n+k*d); k=0,1,2,3,4) in arithmetic progression.

+10
2

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,24

COMMENTS

See A248625 for more information, links and examples.

LINKS

Table of n, a(n) for n=0..91.

PROG

(PARI) a=[]; for(n=1, 190, a=concat(a, 0); while(hasAP(a, 5), a[#a]++)); a \\ See A248625 for hasAP(). Use concat(a, 1) for the "positive integer" variant.