A219109 -id:A219109 - cp's OEIS frontend

A225192 Number of primes p such that p is -1 mod n where p < n-th prime.

0, 0, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 0, 2, 1, 2, 0, 2, 1, 2, 1, 1, 0, 3, 0, 0, 1, 1, 0, 3, 1, 2, 1, 2, 1, 2, 1, 3, 0, 1, 1, 3, 0, 2, 2, 1, 0, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 0, 3, 0, 1, 1, 2, 0, 3, 0, 2, 1, 1, 1, 1, 0, 1, 1, 3, 1, 3, 1, 2, 0, 2, 1, 4, 0, 1, 2

Offset: 1

Irina Gerasimova, May 01 2013

nonn

Primes p(n) such that a(n) = a(n + 1): 2, 5, 17, 19, 23, 73, 97, 103, 173, 193, 233, 239, 263, 293, 347, 349, 353, 373, 449, 467,...
Primes p(n) such that p is not -1 mod n and mod n+1 for all prime p < p(n+1): 2, 97, 829, 1597, 2251,...
Smallest k such that a(k) = n:, 1, 3, 6, 24, 84, 90,...
Numbers n such that a(n) is equal to number of primes p such that n is -1 mod p where p < n-th prime: 1, 2, 3, 4, 7, 8, 10, 14, 15, 20, 22, 28, 31, 32, 34, 40, 44, 45, 46, 50, 52, 55, 57, 63, 65, 70, 72, 87,...

			Prime 11 == - 1 (mod 12), prime 23 == -1 (mod 12) and 11, 23 < prime(12) = 37, so a(12) = 2.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A038700, A219109.

Table[s = Prime[Range[n - 1]]; Length[Select[s, Mod[#, n] == n - 1 &]], {n, 93}] (* T. D. Noe, May 13 2013 *)

a(n)=my(s); forstep(p=n-1,prime(n)-1,n,s+=isprime(p)); s \\ Charles R Greathouse IV, Mar 18 2014

A225318 Numbers n such that either prime(n-1) == -1 (mod n) or prime(n+1) == -1 (mod n) but not both.

Original entry on oeis.org

2, 4, 7, 8, 14, 16, 26, 27, 32, 33, 35, 76, 78, 169, 170, 172, 175, 177, 183, 184, 185, 434, 446, 1054, 1056, 2638, 2702, 6468, 15930, 40069, 40070, 40080, 40112, 40115, 40157, 251721, 251758, 251767, 251770, 251788, 637286, 4124464, 4124704

Offset: 1

Irina Gerasimova, May 05 2013

nonn

			2nd prime is 3 and 2 is a member because 1st prime, 2, is congruent to 0 mod 2 and 3rd prime, 5, is congruent to -1 mod 2;
6th prime is 11 and 6 is not a member because 5th prime, 11, is congruent to -1 mod 6 and 7th prime, 17, is congruent to -1 mod 6;
7th prime is 17 and 7 is a member because 6th prime, 13, is congruent to -1 mod 7 and 8th prime, 19, is congruent to 1 mod 6;
14th prime is 43 and 14 is a member because 13th prime, 41, is congruent to -1 mod 14 and 15th prime, 47, is congruent to 5 mod 14.

Cf. A038700, A045924, A078931, A219109.

for n from 2 to 100000 do
    if modp(ithprime(n-1),n) = modp(-1,n) then
        pn := true ;
    else
        pn := false ;
    end if;
    if modp(ithprime(n+1),n) = modp(-1,n) then
        pm := true ;
    else
        pm := false ;
    end if;
    if pn <> pm then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, May 09 2013

is(n)=my(p=prime(n-1),q=nextprime(nextprime(p+1)+1),v=[p+1,q+1]%n); !vecmin(v) && vecmax(v) \\ Charles R Greathouse IV, Mar 18 2014

Corrected by R. J. Mathar, May 09 2013

a(36)-a(43) from Alois P. Heinz, May 18 2013

cp's OEIS Frontend

A225192 Number of primes p such that p is -1 mod n where p < n-th prime.

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