A072897 Least n-th order digital invariant which is not an Armstrong number (A005188), or 0 if no such term exists.

136, 2178, 58618, 63804, 2755907, 0, 144839908, 304162700, 4370652168, 0, 0, 0, 0, 0, 21914086555935085, 187864919457180831, 0, 13397885590701080090, 0, 0, 0, 19095442247273220984552, 1553298727699254868304830, 1539325689516673750004702, 242402817739393059296681797

Offset: 3

Author

Robert G. Wilson v, Aug 09 2002

Keywords

• hard
• nonn
• base

Comments

An n-th order digital invariant is a number such that the sum of the n-th powers of the digits of n equals some number k and the sum of the n-th powers of the digits of k equals n. An Armstrong number is where n = k.

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, London, England, 1997, pp. 124, 155.

Links

• Tim Johannes Ohrtmann, Table of n, a(n) for n = 3..45
• Eric Weisstein's World of Mathematics, Invariant.

Crossrefs

Cf. A005188, A072409.

Programs

Mathematica

Do[k = 1; While[ !(Apply[Plus, IntegerDigits[Apply[Plus, IntegerDigits[k]^n]]^n] == k && Apply[Plus, IntegerDigits[k]^n] != k), k++ ]; Print[k], {n, 3, 7}]

Extensions

a(8)-a(27) from Tim Johannes Ohrtmann, Aug 27 2015