A099069 Numbers n such that n = prime(d_1*d_2*...*d_k) - phi(d_1 + d_2 + ... + d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

1, 2, 3, 19, 35497

Offset: 1

Author

Farideh Firoozbakht, Oct 29 2004

Keywords

• base
• more
• nonn
• fini

Comments

Sequence is finite since prime(d_1*d_2*...*d_k) <= prime(9^k) <= 9^k(k log 9 + log k + log log 9) < 10^(k-1) for large enough k, i.e., it will have fewer than k digits. In particular, a(n) < 10^69. - Chai Wah Wu, Aug 10 2017

Examples

			35497 is in the sequence because 35497 = prime(3*5*4*9*7) - phi(3 + 5 + 4 + 9 + 7).
		

Links

• C. Rivera, Puzzle 279The Prime Puzzles & Problems connection.

Crossrefs

Cf. A097223, A097227, A099067, A099068.

Programs

Mathematica

Do[h=IntegerDigits[n];l=Length[h];If[ !MemberQ[h, 0]&&n==Prime[Product[h[[k]], {k, l}]]-EulerPhi[Sum[h[[k]], {k, l}]], Print[n]], {n, 6000000}]