A080113 -id:A080113 - cp's OEIS frontend

A080111 Characteristic function of A080113.

1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1

Offset: 1

Antti Karttunen, Feb 11 2003

nonn

Index entries for characteristic functions

Maple
```
A080111 := n -> 1-A080116(A080117(n));
```

A080112 Positions of A080114 in A000040.

Original entry on oeis.org

2, 3, 4, 5, 6, 9, 11, 12, 15, 17, 20, 22, 23, 27, 32, 36, 39, 43, 46, 52, 54, 56, 58, 64, 72, 76, 81, 83, 85, 92, 96, 103, 109, 111, 118, 120, 128, 132, 133, 146, 150, 154, 156, 157, 164, 166, 167, 173, 175, 179, 182, 185, 190, 200, 202, 207, 215, 222, 225, 228, 229

Offset: 1

Antti Karttunen, Feb 11 2003

nonn

Complement of A080113. Characteristic function: A080110.

A080112 := proc(n) option remember; local i; if(1 = n) then RETURN(2); fi; i := A080112(n-1)+1; while(i > 0) do if(A080110(i) > 0) then RETURN(i); fi; i := i+1; od; end;

s[p_, u_] := Sum[JacobiSymbol[j, p], {j, 1, u}]; Select[Range[2, 300], (p = Prime[#]; AllTrue[Range[(p - 1)/2], s[p, #] >= 0 &]) &] (* Jean-François Alcover, Mar 07 2016 *)

@CachedFunction
def A080112(n) :
     if 1 == n : return 2
     i = A080112(n-1) + 1
     while i > 0 :
         if A080110(i) > 0 : return i
         i += 1
[A080112(n) for n in (1..61)] # Peter Luschny, Aug 09 2012

A080115 Primes not in A080114.

Original entry on oeis.org

2, 17, 19, 29, 41, 43, 53, 61, 67, 73, 89, 97, 101, 107, 109, 113, 127, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 223, 227, 229, 233, 241, 257, 269, 277, 281, 283, 293, 307, 313, 317, 331, 337, 347, 349, 353, 367, 373, 379, 389, 397, 401, 409, 421

Offset: 1

Antti Karttunen, Feb 11 2003

nonn

Cf. A080113.

Maple
```
A080115 := n -> ithprime(A080113(n));
```

cp's OEIS Frontend

A080111 Characteristic function of A080113.

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Maple

A080112 Positions of A080114 in A000040.

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Mathematica

Sage

A080115 Primes not in A080114.

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Maple