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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. 2
1, 2, 3, 19, 35497 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..5.

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

EXAMPLE

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

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}]

CROSSREFS

Cf. A097223, A097227, A099067, A099068.

Sequence in context: A066735 A232498 A254380 * A038584 A108022 A108884

Adjacent sequences:  A099066 A099067 A099068 * A099070 A099071 A099072

KEYWORD

base,more,nonn,fini

AUTHOR

Farideh Firoozbakht, Oct 29 2004

STATUS

approved

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Last modified April 7 10:56 EDT 2020. Contains 333301 sequences. (Running on oeis4.)