A336772
Sums s of positive exponents such that no prime of the form 2^j*3^k + 1 with j + k = s exists.
Original entry on oeis.org
12, 24, 33, 46, 48, 60, 72, 74, 80, 96, 102, 111, 118, 120, 130, 132, 141, 142, 144, 147, 159, 162, 165, 166, 168, 186, 200, 216, 234, 240, 242, 252, 258, 288, 306, 309, 312, 318, 358, 370, 374, 375, 384, 399, 405, 408, 414, 420, 432, 435, 462, 464, 468, 478
Offset: 1
a(1) = 12, because none of the 11 numbers {2^1*3^11+1, 2^2*3^10+1, ..., 2^11*3^1+1} = {354295, 236197, 157465, 104977, 69985, 46657, 31105, 20737, 13825, 9217, 6145} is prime,
a(2) = 24: none of the 23 numbers {2^1*3^23+1, 2^2*3^22+1, ..., 2^23*3^1+1} = {188286357655, 125524238437, 83682825625, 55788550417, ..., 56623105, 37748737, 25165825} is prime.
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for(s=2,500, my(t=1); for(j=1,s-1, my(k=s-j); if(isprime(2^j*3^k+1),t=0;break)); if(t,print1(s,", ")))
A337881
30*a(n) - 1 is the least prime of the form 2^r*3^s*5^t - 1, r > 0, s > 0, t > 0, r + s + t = n.
Original entry on oeis.org
1, 2, 6, 8, 16, 48, 96, 432, 384, 512, 2304, 4608, 23040, 8192, 24576, 49152, 65536, 294912, 655360, 1310720, 2621440, 10616832, 6291456, 28311552, 62914560, 75497472, 251658240, 838860800, 402653184, 805306368, 1073741824, 12079595520, 14495514624, 65229815808
Offset: 3
A337882
30*a(n) + 1 is the least prime of the form 2^r*3^s*5^t + 1, r > 0, s > 0, t > 0, r + s + t = n.
Original entry on oeis.org
1, 2, 6, 8, 40, 72, 160, 288, 256, 512, 2560, 2048, 6144, 30720, 24576, 122880, 147456, 737280, 1638400, 1179648, 3932160, 4718592, 21233664, 12582912, 25165824, 382205952, 67108864, 679477248, 1509949440, 805306368, 13589544960, 4831838208, 9663676416, 32212254720
Offset: 3
A337437
a(n) is the least prime of the form 2^j*3^k - 1, j > 0, k > 0, j + k = n. a(n) = 0 if no such prime exists.
Original entry on oeis.org
5, 11, 23, 47, 0, 191, 383, 1151, 0, 6911, 6143, 27647, 0, 73727, 497663, 294911, 0, 786431, 17915903, 10616831, 0, 18874367, 188286357653, 169869311, 0, 39182082047, 10319560703, 4076863487, 0, 7247757311, 32614907903, 495338913791, 0, 51539607551, 1174136684543
Offset: 2
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f:= proc(n) local k, p;
if n mod 4 = 2 and n > 2 then return 0 fi;
for k from 1 to n-1 do
p:= 2^(n-k)*3^k-1;
if isprime(p) then return p fi
od;
0
end proc:
map(f, [$2..40]); # Robert Israel, Sep 01 2020
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for(n=2,36, my(pm=oo); for(j=1,n-1, my(k=n-j,p=2^j*3^k-1);if(isprime(p),pm=min(p,pm))); print1(if(pm==oo,0,pm),", "))
Showing 1-4 of 4 results.