A171493 "Kaprekar quadruples": digits of X^4 taken D at a time sum to X (where D is number of digits in X.)

1, 7, 45, 55, 67, 100, 433, 4950, 5050, 38212, 65068, 190576, 295075, 299035, 310024, 336700, 343333, 394615, 414558, 433566, 448228, 450550, 467236, 475497, 476191, 486486, 499500, 500500, 523513, 534898, 549550, 599743, 622414, 628408, 647362

Offset: 1

Author

Robert Munafo, Dec 10 2009

Keywords

• base
• nonn

Comments

Referred to as "natural" Kaprekar numbers on Munafo webpage because a(n) and the 4 pieces of a(n)^4 must all have the same number of digits (some of which can be leading zeros). Analogous to A053816 for squares, as opposed to A006886 and A045913 which allow irregular divisions.

Examples

			7^4 = 2401 ; 2+4+0+1 = 7. 67^4 = 20151121 ; 20+15+11+21 = 67. 4950^4 = 600372506250000 ; 0600+3725+0625+0000 = 4950.
		

Links

• Robert Gerbicz, Table of n, a(n) for n = 1..10852
• Shyam Sunder Gupta, On Some Marvellous Numbers of Kaprekar, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 9, 275-315.
• R. Munafo, Kaprekar Sequences

Crossrefs

Cf. A006886, A006887, A045913, A053816

Extensions

Added term a(1)=1, Robert Gerbicz, Jul 28 2011