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A267540 Primes p such that p (mod 3) = p (mod 5). 3
2, 17, 31, 47, 61, 107, 137, 151, 167, 181, 197, 211, 227, 241, 257, 271, 317, 331, 347, 421, 467, 541, 557, 571, 587, 601, 617, 631, 647, 661, 677, 691, 751, 797, 811, 827, 857, 887, 947, 977, 991, 1021, 1051, 1097, 1171, 1187, 1201, 1217, 1231, 1277, 1291 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Or primes p such that p (mod 15) = {1, 2}.
Terminal digits in a(7)...a(32) alternate 26 times (7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1). 25 differences between the 2 consecutive terms in this range show patterns as well.
A differenceroot function can generate the terms a(7)...a(32).
LINKS
FORMULA
a(n) = 1/2*((-1)^n*(3*(-1)^n*(10n+81)-1)) with (1<n<10) for a(7)...a(16).
G.f.: (x*(-14x^6-32x^5+16x^4+30x^3-x+14)+17)/((x-1)^2*(x+1)) generates a(2)...a(16), (0<=x<15).
G.f.: (x*(x*(30x*(-2x^4-x^3+x+2)-301)+14)+317)/((x-1)^2*(x+1)) generates a(17)...a(32), (0<=x<16).
MAPLE
select(isprime, [seq(seq(15*i+j, j= 1..2), i=0..10000)]); # Robert Israel, Jan 17 2016
MATHEMATICA
Select[ Prime[ Range[10000]], (Mod[#, 3] == Mod[#, 5]) &] (* Or *)
Select[ Prime[ Range[10000]], 0 < Mod[#, 15] < 3 &]
PROG
(Magma) [p: p in PrimesUpTo(2000) | p mod 3 eq p mod 5]; // Vincenzo Librandi, Jan 17 2016
(PARI) lista(nn) = forprime(p=2, nn, if(p%3 == p%5, print1(p, ", "))); \\ Altug Alkan, Jan 17 2016
CROSSREFS
Sequence in context: A362035 A197186 A063118 * A141068 A162622 A078164
KEYWORD
nonn,easy
AUTHOR
Mikk Heidemaa, Jan 16 2016
EXTENSIONS
More terms from Vincenzo Librandi, Jan 17 2016
STATUS
approved

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Last modified June 23 14:31 EDT 2024. Contains 373651 sequences. (Running on oeis4.)