A293425 Primes of the form 2^a * 3^b * 5^c - 1 for positive a, b, c.

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

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

Cf. A000040, A005105, A030433, A132236, A293194.

Sequence in context: A042662 A128469 A132236 * A158477 A161928 A140340

Adjacent sequences: A293422 A293423 A293424 * A293426 A293427 A293428

Keyword

nonn

Author

Muniru A Asiru, Oct 09 2017

Status

approved