A099067 -id:A099067 - cp's OEIS frontend

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

Farideh Firoozbakht, Oct 29 2004

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

			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)).

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

Cf. A099067, A099069, A097223, A097227.

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}]

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

a(6) from Donovan Johnson, Mar 26 2010

A099069 Numbers n such that n = prime(d_1d_2...*d_k) - phi(d_1 + d_2 + ... + d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

1, 2, 3, 19, 35497

Offset: 1

Farideh Firoozbakht, Oct 29 2004

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

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

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

Cf. A097223, A097227, A099067, A099068.

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}]

cp's OEIS Frontend

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.

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A099069 Numbers n such that n = prime(d_1d_2...*d_k) - phi(d_1 + d_2 + ... + d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

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cp's OEIS Frontend

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.

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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.

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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.

A099069 Numbers n such that n = prime(d_1d_2...*d_k) - phi(d_1 + d_2 + ... + d_k) where d_1 d_2 ... d_k is the decimal expansion of n.