A164676 Primes obtained from other primes by taking the corresponding powers of each digit and adding the result.

2, 31, 257, 283, 823799, 3, 29, 29, 29, 826669, 46687, 29, 826669, 826669, 404197709, 775664521, 7, 387467147, 17600761, 17600761, 7, 311, 16780369, 387467147, 387467147, 17600761, 7, 7, 13, 826699, 388247161, 16823903, 826699, 388247161

Offset

1,1

Comments

This sequence was arrived at by doing the arithmetic on primes in their increasing order.

The sequence treats zero terms as generating a "1" digit; i.e., 0^0 = 1. - Harvey P. Dale, Dec 16 2025

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Dario Alpern, Factorization using the Elliptic Curve Method

Chris Caldwell, The First 10,000 Primes

Example

31 from 23: 2^2 + 3^3 = 31 (prime);
823799 from 47: 4^4 + 7^7 = 823799 (prime);
826669 from 157: 1^1 + 5^5 + 7^7 = 826669 (prime).

Mathematica

Select[Table[With[{c=IntegerDigits[p]/.(0->1)}, Total[c^c]], {p, Prime[Range[500]]}], PrimeQ] (* Harvey P. Dale, Dec 16 2025 *)

Crossrefs

Cf. A000040.

Sequence in context: A223145 A389104 A188225 * A381093 A004307 A268879

Adjacent sequences: A164673 A164674 A164675 * A164677 A164678 A164679

Keyword

base,nonn

Author

Parthasarathy Nambi, Aug 20 2009

Extensions

More terms from Zak Seidov, Aug 21 2009

Status

approved