

A219109


The smallest k such that prime(k) == 1 (mod n).


3



1, 2, 1, 2, 8, 3, 6, 4, 7, 8, 14, 5, 27, 6, 10, 11, 19, 7, 12, 8, 13, 14, 33, 9, 35, 27, 16, 23, 40, 10, 18, 11, 32, 19, 34, 20, 21, 12, 51, 22, 38, 13, 55, 14, 24, 33, 60, 15, 25, 35, 26, 27, 47, 16, 29, 39, 30, 40, 71, 17, 93, 18, 54, 31, 77, 32, 79, 19, 33, 34, 61, 20, 172, 21, 35, 36
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OFFSET

1,2


COMMENTS

Numbers n such that a(n) + 1 = a(n + 1) where the a(n)th prime is not the smaller prime in a twin prime pair: 1, 3, 122, 267, 356, 362, 392, 403, 416, 446, 514, ....
Primes p(n) such that p is not 1 mod n for all prime p < p(n): 2, 3, 11, 31, 41, 59, 83, 97, 101, 109, 167, 191, 211, 277, 283, 313, 331, 367, 419,... Also primes p(n) such that p(n) <= A038700(n).


LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = A000720(A038700(n)).  Joerg Arndt, Apr 16 2013


EXAMPLE

For n = 11, we see that the 14th prime (43), modulo 11 is 10, or 1, so a(11) = 14.


MAPLE

with(numtheory); A219109:=proc(q) local k, n;
for n from 1 to q do k:=1; while (ithprime(k)+1) mod n>0 do k:=k+1; od;
print(k); od; end: A219109(10^6); # Paolo P. Lava, May 02 2013


PROG

(PARI) a(n)=forstep(t=n1, n^99, n, if(isprime(t), return(primepi(t)))) \\ Charles R Greathouse IV, Mar 17 2014


CROSSREFS

Cf. A038700, A221861.
Sequence in context: A140894 A208747 A221878 * A137305 A282885 A242841
Adjacent sequences: A219106 A219107 A219108 * A219110 A219111 A219112


KEYWORD

nonn


AUTHOR

Irina Gerasimova, Apr 11 2013


STATUS

approved



