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A293425 Primes of the form 2^a * 3^b * 5^c - 1 for positive a, b, c. 2
29, 59, 89, 149, 179, 239, 269, 359, 449, 479, 599, 719, 809, 1439, 1499, 1619, 2399, 2699, 2879, 2999, 4049, 4799, 5399, 7499, 8999, 9719, 10799, 11519, 12149, 12959, 13499, 15359, 18749, 20249, 21599, 23039, 25919, 33749, 35999, 40499, 51839, 56249, 59999, 65609, 67499, 69119, 71999 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(n) is congruent to 29 (mod 30).
LINKS
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
Sequence in context: A042662 A128469 A132236 * A158477 A161928 A140340
KEYWORD
nonn
AUTHOR
Muniru A Asiru, Oct 09 2017
STATUS
approved

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Last modified February 24 08:44 EST 2024. Contains 370294 sequences. (Running on oeis4.)