A065789 -id:A065789 - cp's OEIS frontend

A050637 a(1) = 2; a(n+1)^2 is next smallest square ending with a(n)^2.

2, 8, 42, 2458, 310042, 2929997542, 1046218875000310042, 406005268741864709999999997070002458, 50376698115810287966925579573179705000000000000000001046218875000310042

Offset: 1

Patrick De Geest, Jul 15 1999

Cf. A050636, A048560, A050631, A061361.

See A065789 for an essentially identical sequence.

More terms from Ulrich Schimke (ulrschimke(AT)aol.com), Nov 06 2001

A065788 a(1) = 64; for n > 1 a(n) is the smallest square > a(n-1) with a(n-1) forming its final digits.

Original entry on oeis.org

64, 1764, 6041764, 96126041764, 8584885596126041764, 1094573934406914368584885596126041764, 164840278246153785356947805564195221094573934406914368584885596126041764

Offset: 1

Klaus Brockhaus, Nov 19 2001

a(n) = A050636(n+1) for n >= 1.

A050634, A050636, A065689, A065789, A065790.

nxt[n_]:=Module[{k=1},While[!IntegerQ[Sqrt[k*10^IntegerLength[n]+n]],k++];k*10^IntegerLength[n]+n]; NestList[nxt,64,6] (* Harvey P. Dale, Dec 14 2019 *)

A065790 a(1) = 64; for n > 1, a(n) is the smallest integer > 0 such that the concatenation a(n)a(n-1)...a(2)a(1) is a square.

Original entry on oeis.org

64, 17, 604, 9612, 85848855, 109457393440691436, 16484027824615378535694780556419522, 2537811713051483817817710620248313487995814710180147690293469081793581

Offset: 1

Klaus Brockhaus, Nov 19 2001

a(n) = A061361(n+1) for n > 1.

Cf. A061359, A061361, A065691, A065788, A065789.

A065808 Square of n has a smaller square as its final digits.

Original entry on oeis.org

7, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 73, 75, 77, 78, 79, 80, 81, 82, 83, 85, 87, 88

Offset: 1

Klaus Brockhaus, Nov 22 2001

Includes all n >= 7 not == 4 or 6 (mod 10). - Robert Israel, Oct 24 2017

Robert Israel, Table of n, a(n) for n = 1..10000

A065807 gives the corresponding squares.

Cf. A065690, A050635, A050637, A050639, A065777, A065780, A065783, A065786, A065789, A065792.

filter:= n ->
  ormap(t -> issqr(n^2 mod 10^t), [$1..ilog10(n^2)]):
select(filter, [$1..100]); # Robert Israel, Oct 24 2017

ds[n_] := NestWhileList[FromDigits[Rest[IntegerDigits[#]]] &, n, # > 9 &]; Select[Range[4, 88], Or @@ IntegerQ /@ Sqrt[Rest[ds[#^2]]] &] (* Jayanta Basu, Jul 10 2013 *)

a065808(m) = local(k, a, b, d, j, n, r); for(k=1, m, a=length(Str(n))-1; b=1; j=1; n=k^2; while(b, d=divrem(n, 10^j); if(d[1]>0&&issquare(d[2]), b=0; issquare(n, &r); print1(r, ","), if(j

Offset changed to 1 by Robert Israel, Oct 24 2017

cp's OEIS Frontend

A050637 a(1) = 2; a(n+1)^2 is next smallest square ending with a(n)^2.

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A065788 a(1) = 64; for n > 1 a(n) is the smallest square > a(n-1) with a(n-1) forming its final digits.

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A065790 a(1) = 64; for n > 1, a(n) is the smallest integer > 0 such that the concatenation a(n)a(n-1)...a(2)a(1) is a square.

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A065808 Square of n has a smaller square as its final digits.

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