# Duplicated sequences.

reismann at free.fr reismann at free.fr
Thu Feb 15 15:44:40 CET 2007

Dear Neil and Seqfans,

Neil, you rejected two of my sequences six months ago :

%I A000001
%S A000001 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227,
239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821,
827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319,
1427, 1451, 1481, 1487, 1607
%N A000001 Primes for which the weight as defined in A117078 is 3.
%C A000001 These sequence is equal to A001359 - (3) (lesser of twin primes -
(3)).
%Y A000001 A117078, A117563, A001359, A118219
%O A000001 1,1
%K A000001 ,nonn,
%A A000001 Remi Eismann (reismann at free.fr)

Reason: too close of A001359 (lesser of twin primes)

%I A000001
%S A000001 5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947,
977, 1103, 1123, 1187, 1223, 1367, 1511, 1747, 1753, 1907, 2287, 2417, 2677,
2903, 2963, 3307, 3313, 3637, 3733, 4013, 4409, 4457, 4597, 4657, 4691, 4993,
5107, 5113, 5303, 5387, 5393
%N A000001 Let p(i) denote the i-th prime. If 2 p(n) - p(n+1) is a prime, say
p(n-i), then we say that p(n) has level(1,i). Sequence gives primes of
level(1,1).
%C A000001 These sequence is equal to A006562 (Balanced primes).
%Y A000001 A117078, A117563, A125830, A006562, A117876, A125576
%O A000001 1,1
%K A000001 ,nonn,
%A A000001 Remi Eismann (reismann at free.fr)

Reason: the same that A006562

I understand your reasons but these two sequences are very important for my
"classification", my construction and the definitions are really different.
Is it possible to revise your position ?

I already have duplicated sequences :
%I A118219
%S A118219 19,79,109,229,349,379,439,499,739,769,859,1009,1279,1429,1489,1549,
%T A118219
1579,1609,1999,2239,2269,2389,2539,2659,2689,2749,3019,3079,3319,3529,
%U A118219 3919,4129,4519,4639,4729,4789,4969,4999,5479,5569,5689,5779,5839,6199
%N A118219 Primes for which k (the weight) is equal to 5 in A117078.
%A A118219 Remi Eismann (reismann(AT)free.fr), May 14 2006

%I A074822
%S A074822 19,79,109,229,349,379,439,499,739,769,859,1009,1279,1429,1489,1549,
%T A074822
1579,1609,1999,2239,2269,2389,2539,2659,2689,2749,3019,3079,3319,3529,
%U A074822 3919,4129,4519,4639,4729,4789,4969,4999,5479,5569,5689,5779,5839,6199
%N A074822 Primes p(n) such that p(n) + 4 = p(n+1) and p(n) == 9 (mod 10).
%A A074822 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 30 2002
%E A074822 Edited by Robert G. Wilson v (rgwv(AT)rgwv.com) and njas, Oct 03 2002

I think that it is necessary to keep both sequences but Seqfans which
definitions do you prefer ?

Friendly,

Rémi

Remi,   the sequence is the important thing, not the definition.

%I A000001
%S A000001 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227,
239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821,
827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319,
1427, 1451, 1481, 1487, 1607
%N A000001 Primes for which the weight as defined in A117078 is 3.
%C A000001 These sequence is equal to A001359 - (3) (lesser of twin primes -
(3)).
%Y A000001 A117078, A117563, A001359, A118219
%O A000001 1,1
%K A000001 ,nonn,
%A A000001 Remi Eismann (reismann at free.fr)

we have a duplicate of A001359

and the second one is a duplicate of  A006562

The thing to do is to add a comment to those sequences

As for this pair:

%I A118219
%S A118219 19,79,109,229,349,379,439,499,739,769,859,1009,1279,1429,1489,1549,
%T A118219
1579,1609,1999,2239,2269,2389,2539,2659,2689,2749,3019,3079,3319,3529,
%U A118219 3919,4129,4519,4639,4729,4789,4969,4999,5479,5569,5689,5779,5839,6199
%N A118219 Primes for which k (the weight) is equal to 5 in A117078.
%A A118219 Remi Eismann (reismann(AT)free.fr), May 14 2006

%I A074822
%S A074822 19,79,109,229,349,379,439,499,739,769,859,1009,1279,1429,1489,1549,
%T A074822
1579,1609,1999,2239,2269,2389,2539,2659,2689,2749,3019,3079,3319,3529,
%U A074822 3919,4129,4519,4639,4729,4789,4969,4999,5479,5569,5689,5779,5839,6199
%N A074822 Primes p(n) such that p(n) + 4 = p(n+1) and p(n) == 9 (mod 10).
%A A074822 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 30 2002
%E A074822 Edited by Robert G. Wilson v (rgwv(AT)rgwv.com) and njas, Oct 03 2002

, what I will do is merge them under the number A074822.

Neil