OFFSET
1,1
COMMENTS
a(n) is congruent to 29 (mod 30).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 29 = 2^1 * 3^1 * 5^1 - 1.
a(2) = 59 = 2^2 * 3^1 * 5^1 - 1.
a(3) = 89 = 2^1 * 3^2 * 5^1 - 1.
a(4) = 149 = 2^1 * 3^1 * 5^2 - 1.
a(5) = 179 = 2^2 * 3^2 * 5^1 - 1.
list of (a, b, c): (1, 1, 1), (2, 1, 1), (1, 2, 1), (1, 1, 2), (2, 2, 1), (4, 1, 1), (1, 3, 1), (3, 2, 1), (1, 2, 2), (5, 1, 1), (3, 1, 2), (4, 2, 1), (1, 4, 1), (5, 2, 1), (2, 1, 3), (2, 4, 1), ...
MAPLE
N:= 10^6: # to get all terms < N
R:= {}:
for c from 1 to floor(log[5]((N+1)/6)) do
for b from 1 to floor(log[3]((N+1)/2/5^c)) do
R:= R union select(isprime, {seq(2^a*3^b*5^c-1,
a=1..ilog2((N+1)/(3^b*5^c)))})
od od:
sort(convert(R, list)); # Robert Israel, Oct 15 2017
MATHEMATICA
With[{n = 10^5}, Sort@ Select[Flatten@ Table[2^a*3^b*5^c - 1, {a, Log2@ n}, {b, Log[3, n/(2^a)]}, {c, Log[5, n/(2^a*3^b)]}], PrimeQ]] (* Michael De Vlieger, Oct 11 2017 *)
PROG
(GAP) K:=10^5+1;; # to get all terms <= K.
A:=Filtered([1..K], IsPrime);;
A293425:=List(Positions(List(A, i->Elements(Factors(i+1))), [2, 3, 5]), i->A[i]);
(PARI) lista(nn) = {forprime(p=2, nn, f = factor(p+1); if ((vecmax(f[, 1]) <= 5) && (#f~==3), print1(p, ", ")); ); } \\ Michel Marcus, Oct 09 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Muniru A Asiru, Oct 09 2017
STATUS
approved