A066458 Numbers n such that Sum_{d runs through digits of n} d^d = pi(n) (cf. A000720).

12, 22, 132, 34543, 612415, 27236725, 27236752, 311162281, 311163138, 327361548, 9237866583, 17499331217, 17499551725, 36475999489, 36475999498

Offset: 1

Author

Jason Earls, Jan 02 2002

Keywords

• base
• nonn
• fini
• full

Comments

Note that only two terms, namely 34543 & 17499331217 are primes. So we have: 34543=prime(3^3+4^4+5^5+4^4+3^3), 17499331217=prime(1^1+7^7+4^4+9^9+9^9+3^3+3^3+1^1+2^2+1^1+7^7) and there is no other such prime. - Farideh Firoozbakht, Sep 23 2005

Examples

			a(3)=132 because there are exactly 1^1+3^3+2^2 (or 32) prime numbers less than or equal to 132.
		

Links

• C. Caldwell and G. L. Honaker, Jr., Is pi(6521)=6!+5!+2!+1! unique?

Crossrefs

Cf. A105328, A105329.

Programs

Mathematica

Do[ If[ Apply[Plus, IntegerDigits[n]^IntegerDigits[n]] == PrimePi[n], Print[n]], {n, 1, 10^7} ]

Extensions

More terms from Robert G. Wilson v, Jan 15 2002

Terms 27236725 onwards from Farideh Firoozbakht, Apr 21 2005 and Sep 17 2005

Sequence completed by Farideh Firoozbakht, Sep 23 2005