A099068 Numbers n such that n=P(d_1)*P(d_2)*...*P(d_k)+(P(d_1)+P(d_2)+...+P(d_k)) where d_1 d_2 ... d_k is the decimal expansion of n and P(i) is the i-th prime.

23, 119, 428, 918, 1637682, 652827658771

Offset

1,1

Comments

There is no other term up to 15000000.

a(7) > 10^12. [Donovan Johnson, Mar 26 2010]

There are no other terms < 10^44. - Chai Wah Wu, Aug 12 2017

Links

Table of n, a(n) for n=1..6.

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

Example

1637682 is in the sequence because 1637682=
P(1)*P(6)*P(3)*P(7)*P(6)*P(8)*P(2)+(P(1)+P(6)+P(3)+P(7)+P(6)+P(8)+P(2)).

Mathematica

Do[h=IntegerDigits[n]; l=Length[h]; If[ !MemberQ[h, 0]&&n==Product[Prime[h[[k]]], {k, l}]+Sum[Prime[h[[k]]], {k, l}], Print[n]], {n, 15000000}]

Crossrefs

Cf. A099067, A099069, A097223, A097227.

Sequence in context: A367722 A293565 A362569 * A220408 A044355 A044736

Adjacent sequences: A099065 A099066 A099067 * A099069 A099070 A099071

Keyword

base,more,nonn

Author

Farideh Firoozbakht, Oct 29 2004

Extensions

Definition corrected by D. S. McNeil, Mar 14 2009

a(6) from Donovan Johnson, Mar 26 2010

Status

approved