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

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Last modified September 22 17:16 EDT 2020. Contains 337291 sequences. (Running on oeis4.)