cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A099067 Numbers n such that n=P(d_1*d_2*...*d_k) + P(d_1+d_2+...+d_k) where d_1 d_2 ... d_k is the decimal expansion of n and P(i) is the i-th prime.

Original entry on oeis.org

82, 92, 194, 149868
Offset: 1

Views

Author

Farideh Firoozbakht, Oct 08 2004

Keywords

Comments

All terms of this sequence are even. Next term (if it exists) is greater than 25000000.

Examples

			149868 is in the sequence because 149868=149717+151=P(1*4*9*8*6*8)+P(1+4+9+8+6+8).

Crossrefs

Cf. A099068, A099069.

Programs

  • Mathematica
    Do[h=IntegerDigits[n];l=Length[h];If[ !MemberQ[h, 0]&& n==Prime[Product[h[[k]], {k, l}]]+Prime[Sum[h[[k]], {k, l}]], Print[n]], {n, 25000000}]

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.

Original entry on oeis.org

1, 2, 3, 19, 35497
Offset: 1

Views

Author

Farideh Firoozbakht, Oct 29 2004

Keywords

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}]
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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