# [seqfan] Re: help needed editing A175625

Richard Mathar mathar at strw.leidenuniv.nl
Sat Jul 31 23:04:36 CEST 2010

```In response to http://list.seqfan.eu/pipermail/seqfan/2010-July/005469.html

If we select  N(i)=2*i+7; ((2*i+7) mod 3)> 0;
as "Numbers n of the form 2*i+7 which are congruent to 1 or 2 mod 3" we
get A007310 without the 1 and 5, supposing i>=0.
If we further demand that 4^(i+3) == 1 (mod 2i+7) we seem to get
mostly prime numbers n >=7 (?) and in addition nonprimes 341, 1105, 1387,
1729 etc (is this A066488?).
If we furthermore sieve that 4^(i+2) == 1 (mod i+3) then we get for the n:

7,11,23,31,47,59,83,107,167,179,227,263,347,359,383,467,479,503,563,587,683,719,839,863,887,983,1019,1123,1187,1283,1291,1307,1319,1367,1439,1487,1523,1619,1823,1907,2027,2039,2063,2099,2207,2447,2459,2543,2579,2819,2879,2903,2963,2999,3023,3119,3163,3167,3203,3391,3467,3623,3779,3803,3863,3947,4007,4079,4127,4139,4259,4283,4547,4679,4703,4787,4799,4919,4931,5087,5099,5387,5399,5483,5507,5639,5807,5879,5927,5939

So if we say
Members n of A007310 such that 2^(n-1) =1 (mod n) and 2^(n-3) = 1 (mod (n-1)/2)
then we get

7,11,23,31,47,59,83,107,167,179,227,263,347,359,383,467,479,503,563,587,683,719,839,863,887,983,1019,1123,1187,1283,1291,1307,1319,1367,1439,1487,1523,1619,1823,1907,2027,2039,2063,2099,2207,2447,2459,2543,2579,2819,2879,2903,2963,2999,3023,3119,3163,3167,3203,3391,3467,3623,3779,3803,3863,3947,4007,4079,4127,4139,4259,4283,4547,4679,4703,4787,4799,4919,4931,5087,5099,5387,5399,5483,5507,5639,5807,5879,5927,5939

A007310 := proc(n)
option remember;
if n <= 2 then
op(n,[1,5]);
else
procname(n-2)+6 ;
end if;
end proc:

for i from 1 to 2000 do
n := A007310(i) ;
if 2^(n-1) mod n = 1 then
if 2^(n-3) mod ((n-1)/2) = 1 then
printf("%d,",n) ;
end if;
end if;
end do:

```