A049561 -id:A049561 - cp's OEIS frontend

A059256 Primes p such that x^29 = 2 has no solution mod p.

59, 233, 349, 523, 929, 1103, 1277, 1451, 1567, 1741, 1973, 2089, 2437, 2843, 3307, 3539, 4003, 4177, 4409, 4583, 4931, 5279, 5569, 5743, 5801, 6091, 6323, 6961, 7019, 7193, 7309, 7541, 8179, 8237, 8353, 8527, 8933, 9049, 9281, 9397, 9629, 9803

Offset: 1

Klaus Brockhaus, Jan 23 2001

Complement of A049561 relative to A000040.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A049561.

[p: p in PrimesUpTo(10000) | not exists{x : x in ResidueClassRing(p) | x^29 eq 2} ]; // Vincenzo Librandi, Sep 20 2012

ok[p_]:= Reduce[Mod[x^29 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[1300]], ok] (* Vincenzo Librandi, Sep 20 2012  *)

A138980 a(0)=1; for n>=1, a(n) = smallest prime > a(n-1) such that (sum{k=0 to n} a(k)) is composite.

Original entry on oeis.org

1, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281

Offset: 0

Leroy Quet, Apr 05 2008

nonn

Although superficially similar to A049561, the two sequences are in fact quite different (see for example A138982).

R. J. Mathar, Apr 30 2008, Table of n, a(n) for n = 0..112

Cf. A138981, A138982, A049561.

A138980 := proc(n) option remember ; local i,p ; if n = 0 then 1 ; else for p from nextprime(A138980(n-1)) do if isprime(p) then if not isprime( p+add(A138980(i),i=0..n-1) ) then RETURN(p) ; fi ; fi ; od: fi ; end: seq(A138980(n),n=0..120) ; # R. J. Mathar Apr 30 2008

More terms from R. J. Mathar, Apr 30 2008

A138982 Primes not in A138980.

Original entry on oeis.org

2, 59, 163, 283, 311, 313, 383, 461, 541, 587, 619, 653, 857, 991, 1033, 1051, 1069, 1153, 1277, 1367, 1511, 1613, 1693, 1933, 2129, 2179, 2287, 2437, 2473, 2521, 2663, 2731, 2957, 3109, 3167, 3169, 3251, 3343, 3449, 3581, 3631, 3691, 3907, 3919, 4049, 4451, 4639, 4663, 4751, 4793, 5051, 5099, 5227, 5303, 5309, 5381, 5387, 5449, 5521, 5701, 6043, 6091, 6247, 6361, 6451, 6823, 7309, 7393, 7411, 7489, 7541, 7547, 7589, 7759, 7901, 8377, 8501, 8513, 9227, 9281, 9311, 9769

Offset: 1

Leroy Quet and M. F. Hasler, Apr 05 2008

nonn

Except for the first term, the sequences A049561 and A138980 both consist of all odd primes except for 59, up to p=163 which is in A049561 but not in A138980.

Cf. A138980, A138981.

s=a=1;for(i=1,10^3,/*print1(","a);*/ while(isprime( s+a=nextprime(a+1) ),print1(a","));s+=a) /*using instead the commented-out print() command yields the sequence A138980.*/

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A059256 Primes p such that x^29 = 2 has no solution mod p.

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A138980 a(0)=1; for n>=1, a(n) = smallest prime > a(n-1) such that (sum{k=0 to n} a(k)) is composite.

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A138982 Primes not in A138980.

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