A088081 Smallest prime(k) such that for every r = 1 to n, there exist i,j, k >= j > i, such that prime(j)-prime(i) == 0 ( mod r).

3, 5, 5, 7, 7, 11, 17, 17, 17, 17, 17, 17, 29, 29, 29, 29, 29, 29, 41, 41, 41, 41, 53, 53, 53, 53, 53, 53, 53, 53, 67, 67, 71, 71, 71, 71, 79, 79, 79, 79, 79, 79, 89, 89, 89, 89, 97, 97, 101, 101, 101, 101, 109, 109, 113, 113, 113, 113, 113, 113, 127, 127, 131, 131, 131

Offset

1,1

Links

Table of n, a(n) for n=1..65.

Example

a(11) = a(12) = 17, but a(13) = 29 as 29-3 == 0 (mod 13). And we have
5-3 = 2, 11-5 = 2*3, 7-3 = 4, 7-2 = 5, 11-5 = 6, 17-3 = 2*7, 11-3 = 8, 23-5 = 2*9, 13-3 = 10, 13 - 2 = 11, 17-5 = 12, 29-3 = 2*13.

Prog

(PARI) found = vector(500); x = 1; forprime(p = 3, 500, oldX = x; forprime (q = 2, p - 1, v = divisors(p - q); for (i = 1, length(v), found[v[i]] = 1; if (v[i] == x, while (found[x], x++; write1("A088081.txt", p" "))))); if (oldX != x, write1("A088083.txt", p" "); write1("A088082.txt", x - 1" "))); \\ David Wasserman, Jul 11 2005

Crossrefs

Cf. A088082.

Cf. A088083.

Sequence in context: A087821 A204894 A109258 * A206768 A168322 A138475

Adjacent sequences: A088078 A088079 A088080 * A088082 A088083 A088084

Keyword

nonn

Author

Amarnath Murthy, Sep 22 2003

Extensions

More terms from David Wasserman, Jul 11 2005

Status

approved