A066631 -id:A066631 - cp's OEIS frontend

A112086 a(n) = the period of the first differences of the n-th row of A112060 (or A112070), or 0 if that row does not have a periodic first difference.

2, 4, 6, 16, 72, 420, 3240

Offset: 1

Antti Karttunen, Aug 28 2005

These values have been computed empirically. An independent recomputation or a mathematical proof would be welcome. The initial terms factored: 2, 2*2, 2*3, 2*2*2*3*3, 2*2*7*3*5, 2*2*2*3*3*3*3*5, ...

These are the periods of A010684, A112132, A112133, A112134, A112135, A112136, A112137, etc. (Periods of A112138 & A112139 not computed yet.) If we sum the period length prefixes of these sequences, as Sum_{i=1..a(1)} A010684(i), Sum_{i=1..a(2)} A112132(i), Sum_{i=1..a(3)} A112133(i), etc., we get the sequence 4, 12, 60, 420, 4620, 60060, 1021020, ... (cf. A097250) and when doubled, it yields: 8, 24, 120, 840, 9240, 120120, 2042040, ... (cf. A066631 and A102476).

A068192 Let a(1)=2, f(n) = 4a(1)a(2)...a(n-1) for n >= 1 and a(n) = f(n)-prevprime(f(n)-1) for n >= 2, where prevprime(x) is the largest prime < x.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 31, 29, 23, 41, 43, 37, 89, 59, 53, 67, 79, 71, 137, 109, 239, 167, 199, 47, 83, 97, 61, 373, 101, 179, 193, 131, 151, 73, 263, 593, 139, 113, 157, 103, 241, 181, 397, 233, 617, 311, 191, 229, 271, 269, 127, 223, 331, 337, 211, 163

Offset: 1

Frank Buss (fb(AT)frank-buss.de), Feb 19 2002

nonn

The terms are easily seen to be distinct. It is conjectured that every element is prime. Do all primes occur in the sequence?

First 1000 terms are primes. - Mauro Fiorentini, Aug 01 2020

Mauro Fiorentini, Table of n, a(n) for n = 1..1000

Cf. A068193 has the indices of the primes in this sequence. A066631 has the sequence of f's. Also see A067836.

Mathematica
```
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```

f := 4:for n from 1 to 50 do a := f-numlib::prevprime(f-2):f := f*a:print(a) end_for

Edited by Dean Hickerson, Jun 10 2002

cp's OEIS Frontend

A112086 a(n) = the period of the first differences of the n-th row of A112060 (or A112070), or 0 if that row does not have a periodic first difference.

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A068192 Let a(1)=2, f(n) = 4a(1)a(2)...a(n-1) for n >= 1 and a(n) = f(n)-prevprime(f(n)-1) for n >= 2, where prevprime(x) is the largest prime < x.

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Author

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Mathematica

MuPAD

Extensions

cp's OEIS Frontend

A112086 a(n) = the period of the first differences of the n-th row of A112060 (or A112070), or 0 if that row does not have a periodic first difference.

Views

Author

Keywords

Comments

Crossrefs

A068192 Let a(1)=2, f(n) = 4*a(1)*a(2)*...*a(n-1) for n >= 1 and a(n) = f(n)-prevprime(f(n)-1) for n >= 2, where prevprime(x) is the largest prime < x.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

MuPAD

Extensions

A068192 Let a(1)=2, f(n) = 4a(1)a(2)...a(n-1) for n >= 1 and a(n) = f(n)-prevprime(f(n)-1) for n >= 2, where prevprime(x) is the largest prime < x.