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A023145
Numbers k such that prime(k) == 3 (mod k).
13
1, 2, 4, 7, 8, 31, 32, 34, 74, 76, 1052, 6455, 15928, 251707, 251765, 4124458, 27067012, 27067120, 69709718, 69709871, 69709877, 69709934, 69709943, 69709954, 69709963, 69709964, 465769810, 8179002124, 145935689390, 382465573486, 885992692751818, 885992692751822
OFFSET
1,2
LINKS
EXAMPLE
204475053103 = prime(8179002124) and 204475053103 = 25*8179002124 + 3.
MATHEMATICA
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[ Mod[p = NextPrim[p], n] == 3, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)
Select[Range[100000], Mod[Prime[#] - 3, #] == 0 &] (* T. D. Noe, Feb 05 2013 *)
PROG
(Sage)
def A023145(max) :
terms = []
p = 2
for n in range(1, max+1) :
if (p - 3) % n == 0 : terms.append(n)
p = next_prime(p)
return terms
# Eric M. Schmidt, Feb 05 2013
KEYWORD
nonn
EXTENSIONS
More terms from Robert G. Wilson v, Feb 18 2004
2 more terms from Giovanni Resta, Feb 22 2006
a(29) from Robert G. Wilson v, Feb 22 2006
First two terms inserted by Eric M. Schmidt, Feb 05 2013
Terms a(30) and beyond from Giovanni Resta, Feb 23 2020
STATUS
approved