This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A023110 Squares which remain squares when the last digit is removed. 30
 0, 1, 4, 9, 16, 49, 169, 256, 361, 1444, 3249, 18496, 64009, 237169, 364816, 519841, 2079364, 4678569, 26666896, 92294449, 341991049, 526060096, 749609641, 2998438564, 6746486769, 38453641216, 133088524969, 493150849009, 758578289296, 1080936581761 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This A023110 = A031149^2 is the base 10 version of A001541^2 = A055792 (base 2), A001075^2 = A055793 (base 3), A004275^2 = A055808 (base 4), A204520^2 = A055812 (base 5), A204518^2 = A055851 (base 6), A204516^2 = A055859 (base 7), A204514^2 = A055872 (base 8) and A204502^2 = A204503 (base 9). - M. F. Hasler, Sep 28 2014 For the first 4 terms the square has only one digit. It is understood that deleting this digit yields 0. - Colin Barker, Dec 31 2017 REFERENCES R. K. Guy, Neg and Reg, preprint, Jan 2012. LINKS Dmitry Petukhov, Table of n, a(n) for n = 1..67 [Terms 1 to 38 by David W. Wilson; terms 39 to 40 by Robert G. Wilson v, Jan 16 2012; terms 41 to 67 by Dmitry Petukhov, Feb 12 2016] M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012 FORMULA Appears to satisfy a(n)=1444*a(n-7)+a(n-14)-76*sqrt(a(n-7)*a(n-14)) for n >= 16. For n = 15, 14, 13, ... this would require a(1) = 16, a(0) = 49, a(-1) = 169, ... - Henry Bottomley, May 08 2001 a(n) = A031149(n)^2. - M. F. Hasler, Sep 28 2014 Conjectures from Colin Barker, Dec 31 2017: (Start) G.f.: x^2*(1 + 4*x + 9*x^2 + 16*x^3 + 49*x^4 + 169*x^5 + 256*x^6 - 1082*x^7 - 4328*x^8 - 9738*x^9 - 4592*x^10 - 6698*x^11 - 6698*x^12 - 4592*x^13 + 361*x^14 + 1444*x^15 + 3249*x^16 + 256*x^17 + 169*x^18 + 49*x^19 + 16*x^20) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1 - 1442*x^7 + x^14)). a(n) = 1443*a(n-7) - 1443*a(n-14) + a(n-21) for n>22. (End) MAPLE count:= 1: A[1]:= 0: for n from 0 while count < 35 do   for t in [1, 4, 6, 9] do     if issqr(10*n^2+t) then        count:= count+1;        A[count]:= 10*n^2+t;     fi   od od: seq(A[i], i=1..count); # Robert Israel, Sep 28 2014 MATHEMATICA fQ[n_] := IntegerQ@ Sqrt@ Quotient[n^2, 10]; Select[ Range@ 1000000, fQ]^2 (* Robert G. Wilson v, Jan 15 2011 *) PROG (PARI) for(n=0, 1e7, issquare(n^2\10) & print1(n^2", ")) \\  M. F. Hasler, Jan 16 2012 CROSSREFS Cf. A023111. Cf. A031150, A053784, A031149, A055792, A055793, A055808, A055812, A055851, A055859, A055872. Cf. A001541, A001075, A004275, A204520, A204518, A204516, A204514, A204502, A204503. Sequence in context: A059931 A027382 A164840 * A277699 A073723 A161493 Adjacent sequences:  A023107 A023108 A023109 * A023111 A023112 A023113 KEYWORD nonn,base AUTHOR EXTENSIONS More terms from M. F. Hasler, Jan 16 2012 Henry Bottomley's comment edited by Robert Israel, Sep 28 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 16 08:42 EST 2018. Contains 318158 sequences. (Running on oeis4.)