A144360
Primes of the form 8^k + 7. Also, primes of the form 64^m + 7.
Original entry on oeis.org
71, 262151, 1073741831, 302231454903657293676551, 85070591730234615865843651857942052871, 23945242826029513411849172299223580994042798784118791, 25711008708143844408671393477458601640355247900524685364822023
Offset: 1
71 - 1 = 70 is the fourth triskaidecagonal number and seventh pentagonal number.
Cf.
A000040,
A000668,
A144231,
A144232,
A144233,
A144234,
A144236,
A144242,
A144245,
A144246,
A144247,
A144313.
A144236
Prime numbers of the form 7^k +- 6.
Original entry on oeis.org
13, 43, 337, 349, 117643, 40353601, 33232930569607, 558545864083284001, 1341068619663964900801, 7730993719707444524137094401, 2651730845859653471779023381607, 256923577521058878088611477224235621321601, 4318114567396436564035293097707728087552248843
Offset: 1
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Select[Flatten[Table[7^k+{6,-6},{k,40}]],PrimeQ]//Sort (* Harvey P. Dale, Jul 07 2021 *)
A144242
Prime numbers of the form 8^k +- 7.
Original entry on oeis.org
71, 262151, 1073741831, 549755813881, 302231454903657293676551, 85070591730234615865843651857942052871, 23945242826029513411849172299223580994042798784118791, 25711008708143844408671393477458601640355247900524685364822023
Offset: 1
-
Select[Sort[Flatten[Table[8^k+{7,-7},{k,90}]]],PrimeQ] (* Harvey P. Dale, Aug 08 2016 *)
A144245
Prime numbers of the form 9^k +- 8.
Original entry on oeis.org
17, 73, 89, 6553, 6569, 4782961, 4782977, 3486784393, 3486784409, 31381059601, 1350851717672992097, 984770902183611232889, 381520424476945831628649898801, 969773729787523602876821942164080815560169, 145557834293068928043467566190278008218249525830565939618489
Offset: 1
A144246
Prime numbers of the form 10^k +- 9.
Original entry on oeis.org
19, 109, 991, 1009, 10009, 99991, 9999991, 1000000009, 1000000000000000009, 10000000000000000000009, 999999999999999999999999999999991, 999999999999999999999999999999999999999999991, 1000000000000000000000000000000000000000000009
Offset: 1
-
Select[Sort[Flatten[Table[10^n+{9,-9},{n,50}]]],PrimeQ] (* Harvey P. Dale, Jul 22 2016 *)
A144247
Prime numbers of the form 11^k +- 10.
Original entry on oeis.org
131, 1321, 214358891, 505447028499293761, 5559917313492231491, 895430243255237372246521, 20796505671840591460586660430317517562942313712635618374571, 539407797827634189900210968137750826278309533633974732577186113975171
Offset: 1
A264734
Prime powers k such that k - 2 and k + 2 are prime powers.
Original entry on oeis.org
3, 5, 7, 9, 11, 25, 27, 29, 81, 241, 59051, 450283905890997361, 36472996377170786401
Offset: 1
81 is in this sequence because 81 - 2 = 79, 81 and 81 + 2 = 83 are all prime powers.
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[n: n in [5..100000] | IsPrimePower(n-2) and IsPrimePower(n) and IsPrimePower(n+2)];
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ispp:= proc(x) local p, r;
if isprime(x) then return true fi;
p:= 2;
do
r:= iroot(x,p);
if r^p = x then return isprime(r) fi;
if r < 2 then return false fi;
p:= nextprime(p);
od:
end proc:
ispp(1):= true:
A:= NULL;
for n from 1 to 1000 do
B:= map(ispp, [3^n-4,3^n-2,3^n+2,3^n+4]);
if B[1] and B[2] then A:= A, 3^n-2 fi;
if B[2] and B[3] then A:= A, 3^n fi;
if B[3] and B[4] then A:= A, 3^n+2 fi;
od:
A; # Robert Israel, Nov 22 2015
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Prepend[Select[Range@ 100000, AllTrue[{# - 2, #, # + 2}, PrimePowerQ] &], 3] (* Michael De Vlieger, Dec 03 2015, Version 10 *)
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is(k) = isprimepower(k) || k==1;
for(k=1, 1e6, if(is(k) && is(k+2) && is(k-2), print1(k, ", "))) \\ Altug Alkan, Nov 22 2015
Showing 1-7 of 7 results.
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