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 A031150 Appending a digit to n^2 gives another perfect square. 10
 1, 2, 4, 5, 6, 12, 18, 43, 80, 154, 191, 228, 456, 684, 1633, 3038, 5848, 7253, 8658, 17316, 25974, 62011, 115364, 222070, 275423, 328776, 657552, 986328, 2354785, 4380794, 8432812, 10458821, 12484830, 24969660, 37454490 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Square root of 'Squares from A023110 with last digit removed'. One could include an initial '0', and even list it with multiplicity 3 or 4, since 00, 01, 04 and 09 are all perfect squares: In analogy to corresponding sequences for other bases, this sequence could be defined as sqrt(floor[A023110/10]), see A204512 [base 8], A204517 (base 7), A204519 (base 6), A204521 [base 5], A001353 [base 3], A001542 [base 2]. (For bases 4 and 9, the corresponding sequence contains all integers.) - M. F. Hasler, Jan 16 2012 REFERENCES R. K. Guy, Neg and Reg, preprint, Jan 2012. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012 Joshua Stucky, Pell's Equation and Truncated Squares, Number Theory Seminar, Kansas State University, Feb 19 2018. Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,38,0,0,0,0,0,0,-1). FORMULA G.f.: x*(x^10+2*x^9+4*x^8+5*x^7+18*x^6+12*x^5+6*x^4+5*x^3+4*x^2+2*x+1) / (x^14-38*x^7+1). - Colin Barker, Jan 30 2013 EXAMPLE 5^2 = 25 and 16^2 = 256, so 5 is in the sequence. 115364^2 = 13308852496, 364813^2 = 133088524969. MAPLE for i from 1 to 150000 do if (floor(sqrt(10 * i^2 + 9)) > floor(sqrt(10 * i^2))) then print(i) end if end do; MATHEMATICA CoefficientList[Series[(x^10 + 2 x^9 + 4 x^8 + 5 x^7 + 18 x^6 + 12 x^5 + 6 x^4 + 5 x^3 + 4 x^2 + 2 x + 1)/(x^14 - 38 x^7 + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 19 2013 *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, -1}, {1, 2, 4, 5, 6, 12, 18, 43, 80, 154, 191, 228, 456, 684}, 40] (* Harvey P. Dale, Jun 09 2017 *) CROSSREFS Cf. A023110, A030686, A030687, A053784. See A202303 for the resulting squares. Sequence in context: A276001 A182109 A006539 * A125775 A331624 A191165 Adjacent sequences:  A031147 A031148 A031149 * A031151 A031152 A031153 KEYWORD nonn,base,easy AUTHOR STATUS approved

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Last modified October 4 12:43 EDT 2022. Contains 357239 sequences. (Running on oeis4.)