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A244660
Numbers x such that the base 10 representation of x^2 forms an arithmetic sequence when split into equal-sized chunks.
1
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
OFFSET
1,1
COMMENTS
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).
EXAMPLE
11142^2 = 124144164 and 124,144,164 is an arithmetic sequence.
PROG
(Python)
from itertools import count
.
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
.
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
CROSSREFS
Sequence in context: A073038 A107650 A291705 * A205751 A205473 A250687
KEYWORD
nonn,base
AUTHOR
Christian Perfect, Jul 04 2014
STATUS
approved