A050639 -id:A050639 - cp's OEIS frontend

A050638 a(n+1) is next smallest square ending with a(n), initial term is 9.

9, 49, 1849, 1671849, 24011671849, 408646172724011671849, 14079962896835441528408646172724011671849, 30988070410883251650062468506470600085614079962896835441528408646172724011671849

Offset: 1

Patrick De Geest, Jul 15 1999

Cf. A050639, A048561, A050630.

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

A061363 a(1) = 9; a(n) = least number such that the concatenation a(n)a(n-1)...a(2)a(1) is a square.

Original entry on oeis.org

9, 4, 18, 167, 2401, 4086461727, 14079962896835441528, 309880704108832516500624685064706000856, 4681896102766617737298881383797502847166028831212571921983062786215145771871779

Offset: 1

Amarnath Murthy, Apr 28 2001

			a(3)a(2)a(1) = 1849 = 43^2, a(4)a(3)a(2)a(1) = 1671849 = 1293^2.

Cf. A050638, A050639, A061359, A061361.

Corrected by Larry Reeves (larryr(AT)acm.org), May 07 2001

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

A050633 a(1)=3; for n>1, a(n)^2 is next smallest nontrivial square containing a(n-1)^2 as a substring.

Original entry on oeis.org

3, 7, 43, 136, 10158, 85927342, 738024797793593

Offset: 1

Patrick De Geest, Jul 15 1999

Starting with a(2)=7, the sequence is identical to A050631.

Cf. A050632, A048562, A050639.

a(n) = sqrt(A050632(n)).

a(7) from Max Alekseyev, Feb 15 2012

A065786 a(1) = 7; for n > 1, a(n) is the square root of the smallest square > a(n-1)^2 with a(n-1)^2 forming its final digits.

Original entry on oeis.org

7, 43, 1293, 154957, 20214998707, 118659019449999845043, 5566692951015284052000000000020214998707, 21637689578064053873124753714430240419600000000000000000000118659019449999845043

Offset: 1

Klaus Brockhaus, Nov 19 2001

a(n) = A050639(n+1) for n >= 1.

Cf. A050635, A050639, A065690, A065785, A065787.

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

A050638 a(n+1) is next smallest square ending with a(n), initial term is 9.

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A061363 a(1) = 9; a(n) = least number such that the concatenation a(n)a(n-1)...a(2)a(1) is a square.

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A050633 a(1)=3; for n>1, a(n)^2 is next smallest nontrivial square containing a(n-1)^2 as a substring.

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Extensions

A065786 a(1) = 7; for n > 1, a(n) is the square root of the smallest square > a(n-1)^2 with a(n-1)^2 forming its final digits.

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

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