# [seqfan] Re: A175075 A094743 repeated modulo operation or differences on primes: duplicates?

Robert G. Wilson v rgwv at rgwv.com
Mon Aug 9 19:05:33 CEST 2010

```Et al,

Yes they are the same. The sequence A094743 comment correctly states
that this sequence contains only 2 with the larger member of the twin
primes. f[s_List] := Block[{p = NextPrime@ s[[-1]]}, While[ !PrimeQ[p - 2],
p = NextPrime at p]; Append[s, p]]; Nest[f, {2}, 50]

Then we only need to show that the sequence A175075 has the same set of
primes.  Obviously if q == p + 2, then p&q are twin primes and q satisfies
the criteria. If q is some other prime then the distance above p = 2*k, k
being any integer > 1. Since taking {r mod (max prime p < r)} results in an
odd parity, this iteration can never end at 2. fQ[p_] := Block[{r = p},
While[r > 2, r = Mod[r, NextPrime[r, -1]]]; r == 2]; Select[ Prime@ Range@
253, fQ]

Sincerely yours, Bob.

--------------------------------------------------
From: "Richard Mathar" <mathar at strw.leidenuniv.nl>
Sent: Monday, August 09, 2010 8:58 AM
To: <seqfan at seqfan.eu>
Subject: [seqfan] A175075 A094743 repeated modulo operation or differences
on primes: duplicates?

>
> Are these two sequences the same?
>
> http://oeis.org/classic/?q=id:A175075|id:A094743
>
> 2,5,7,13,19,31,43,61,73,103,109,139,151,181,193,199,229,241,271,283,313,349,421,433,463,523,571,601,619,643,661,811,823,829,859,883,1021,
>
> 2,5,7,13,19,31,43,61,73,103,109,139,151,181,193,199,229,241,271,283,313,349,421,433,463,523,571,601,619,643,661,811,823,829,859,883,1021,1033,1051,1063,1093,1153,1231,1279,1291,1303,1321,1429,1453,1483,1489,
>
>
>
>
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>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```