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A244660
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Numbers x such that the base 10 representation of x^2 forms an arithmetic sequence when split into equal-sized chunks.
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1
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11142, 11553, 14088, 16713, 18801, 22284, 23097, 23718, 26787, 28818, 323589, 327939, 328992, 416103, 438357, 459069, 502149, 595194, 617928, 647178, 656457, 665853, 677019, 682230, 747099, 767748, 775782, 799233, 813861, 832986, 847266, 855897, 858648, 862014, 924366, 970767, 10174023, 10240146
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OFFSET
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1,1
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COMMENTS
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This sequence only includes numbers which produce arithmetic sequences of at least three terms (and in fact, no squares containing sequences of more than three terms have been found).
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LINKS
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EXAMPLE
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11142^2 = 124144164 and 124,144,164 is an arithmetic sequence.
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PROG
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(Python)
from itertools import count
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def check(n, power):
...np = str(n**power)
...l=len(np)
...for chunks in range(3, 5):
......if l%chunks==0:
.........step = l//chunks
.........bits = [int(np[i:i+step]) for i in range(0, l, step)]
.........diff = bits[1]-bits[0]
.........old=bits[1]
.........go = True
.........for bit in bits[2:]:
............if bit-old!=diff:
...............go=False
...............break
............old = bit
.........if go:
............return True
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for n in count(1):
...if check(n, 2):
......print(n)
(PARI) isoneap(vch) = {r = vch[2] - vch[1]; for (i=3, #vch, if (vch[i] - vch[i-1] != r, return (0)); ); return (1); }
isap(vd, nch, nd) = {npch = nd/nch; vch = vector(nch); ich = 1; inew = 1; for (i=1, nd, if (inew, vch[ich] = vd[i]; inew = 0; , vch[ich] = 10*vch[ich] + vd[i]); if ((i % npch) == 0, ich++; inew = 1); ); isoneap(vch); }
isok(n) = {vd = digits(n^2); nd = #vd; if (isprime(nd), return(0)); ok = 0; fordiv(nd, nch, if (nch > 2, if(isap(vd, nch, nd), return (1))); ); return (0); } \\ Michel Marcus, Jul 06 2014
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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