A293425 - OEIS

%I #17 Oct 15 2017 15:27:46

%S 29,59,89,149,179,239,269,359,449,479,599,719,809,1439,1499,1619,2399,

%T 2699,2879,2999,4049,4799,5399,7499,8999,9719,10799,11519,12149,12959,

%U 13499,15359,18749,20249,21599,23039,25919,33749,35999,40499,51839,56249,59999,65609,67499,69119,71999

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

%C a(n) is congruent to 29 (mod 30).

%H Robert Israel, <a href="/A293425/b293425.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 29 = 2^1 * 3^1 * 5^1 - 1.

%e a(2) = 59 = 2^2 * 3^1 * 5^1 - 1.

%e a(3) = 89 = 2^1 * 3^2 * 5^1 - 1.

%e a(4) = 149 = 2^1 * 3^1 * 5^2 - 1.

%e a(5) = 179 = 2^2 * 3^2 * 5^1 - 1.

%e 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), ...

%p N:= 10^6: # to get all terms < N

%p R:= {}:

%p for c from 1 to floor(log[5]((N+1)/6)) do

%p for b from 1 to floor(log[3]((N+1)/2/5^c)) do

%p      R:= R union select(isprime, {seq(2^a*3^b*5^c-1,

%p              a=1..ilog2((N+1)/(3^b*5^c)))})

%p od od:

%p sort(convert(R,list)); # _Robert Israel_, Oct 15 2017

%t 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 *)

%o (GAP) K:=10^5+1;; # to get all terms <= K.

%o A:=Filtered([1..K],IsPrime);;

%o A293425:=List(Positions(List(A,i->Elements(Factors(i+1))),[2,3,5]),i->A[i]);

%o (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

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

%K nonn

%O 1,1

%A _Muniru A Asiru_, Oct 09 2017