A274620 If n^2 has an even number of digits, write n after the left half of the digits of n^2 and before the right half, otherwise if n^2 has 2t+1 digits, write n after the first t digits of n^2 and before the last t+1 digits.

11, 24, 39, 146, 255, 366, 479, 684, 891, 11000, 11121, 11244, 11369, 11496, 21525, 21656, 21789, 31824, 31961, 42000, 42141, 42284, 52329, 52476, 62525, 62676, 72729, 72884, 82941, 93000, 93161, 103224, 103389, 113456, 123525, 123696, 133769, 143844, 153921, 164000

Offset: 1

Author

N. J. A. Sloane, Jul 03 2016

Keywords

• nonn
• base

Comments

In short, write n in the middle of n^2.

Portions of this sequence are sometimes given as puzzles.

Examples

			4^2 = 16 so a(4) = 1.4.6 = 146.
19^2 = 361 so a(19) = 3.19.61 = 31961.
		

References

• J. A. Reeds, Personal communication to N. J. A. Sloane, Jun 04 2016

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053061, A055436.

Programs

Mathematica

nterms=100;Table[FromDigits[Flatten[Insert[d=IntegerDigits[n^2],IntegerDigits[n],Floor[Length[d]/2]+1]]],{n,nterms}] (* Paolo Xausa, Nov 24 2021 *)

Python

def a(n):
    ss = str(n*n)
    t = len(ss)//2
    return int(ss[:t] + str(n) + ss[t:])
print([a(n) for n in range(1, 41)]) # Michael S. Branicky, Nov 24 2021