A244660 Numbers x such that the base 10 representation of x^2 forms an arithmetic sequence when split into equal-sized chunks.

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).

Links

Michel Marcus, Table of n, a(n) for n = 1..142 (up to 10^8)

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

Adjacent sequences: A244657 A244658 A244659 * A244661 A244662 A244663

Keyword

nonn,base

Author

Christian Perfect, Jul 04 2014

Status

approved