Alan Frank - cp's OEIS frontend

User: Alan Frank

Alan Frank has authored 2 sequences.

A157425 Numbers which can be represented using fewer symbols than the number of decimal digits in the number.

120, 125, 128, 216, 243, 256, 343, 512, 625, 720, 729, 1000, 1024, 1089, 1156, 1225, 1296, 1331, 1369, 1444, 1521, 1600, 1681, 1728, 1764, 1849, 1936, 2025, 2048, 2116, 2187, 2197, 2209, 2304, 2401, 2500, 2601, 2704, 2744, 2809, 2916, 3025, 3125, 3136

Offset: 1

Alan Frank, Feb 28 2009

The "up-arrow" symbol is free, since that is indicated by a superscript.

Additional terms are possible if the double factorial (!!) operator is permitted. [From Sean A. Irvine, Mar 14 2010]

			120=5!, 125=5^3, ..., 59050 = 9^5 + 1, ..., 1354984 = 9^6 + 7^7, ...

Edited by N. J. A. Sloane, Mar 27 2009

Corrected and extended by Sean A. Irvine, Mar 14 2010

A171385 Sum of a positive square and a positive cube in at least three ways.

Original entry on oeis.org

1025, 1737, 2089, 2628, 2817, 3033, 3664, 4481, 4825, 4977, 5841, 7057, 7785, 7948, 8225, 8289, 8900, 10025, 11025, 11665, 12393, 14049, 14400, 14724, 15193, 15345, 15641, 15689, 15884, 16649, 16857, 18201, 18369, 19225, 19664, 19908, 20224

Offset: 1

Alan Frank, Dec 07 2009

Four or more representations have 1025, 19225, 27289, 29025, 39329, 48025, 54225, 65537, 65600, 79129, 92025, 93241, 105192, 105633, 111681, ... - R. J. Mathar, Dec 11 2009

			1025 = 32^2 + 1^3, 31^2 + 4^3, 30^2 + 5^3, and 5^2 + 10^3;
1737 = 35^2 + 8^3, 3^2 + 12^3, and 39^2 + 6^3.

Cf. A054402, integers with two or more such representations.

isA171385 := proc(n) a := 0 ; for c from 1 do if c^3 >= n then break; else if issqr(n-c^3) then a := a+1 ; end if; end if; end do ; a >= 3 ; end proc: for n from 2 to 120000 do if isA171385(n) then printf("%d,",n) ; fi; end do ; # R. J. Mathar, Dec 11 2009

More terms from R. J. Mathar, Dec 11 2009

cp's OEIS Frontend

User: Alan Frank

A157425 Numbers which can be represented using fewer symbols than the number of decimal digits in the number.

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