A128066
Numbers k such that (3^k + 4^k)/7 is prime.
Original entry on oeis.org
3, 5, 19, 37, 173, 211, 227, 619, 977, 1237, 2437, 5741, 13463, 23929, 81223, 121271
Offset: 1
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a:=proc(n) if type((3^n+4^n)/7,integer)=true and isprime((3^n+4^n)/7)=true then n else fi end: seq(a(n),n=1..1500); # Emeric Deutsch, Feb 17 2007
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Do[ p=Prime[n]; f=(3^p+4^p)/(4+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
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f(n)=(3^n + 4^n)/7;
forprime(n=3,10^5,if(ispseudoprime(f(n)),print1(n,", ")))
/* Joerg Arndt, Mar 27 2011 */
Two more terms (13463 and 23929) found by Lelio R Paula in 2008 corresponding to probable primes with 8105 and 14406 digits.
Jean-Louis Charton, Oct 06 2010
Two more terms (81223 and 121271) found by Jean-Louis Charton in March 2011 corresponding to probable primes with 48901 and 73012 digits
A128071
Numbers k such that (3^k + 13^k)/16 is prime.
Original entry on oeis.org
3, 7, 127, 2467, 3121, 34313
Offset: 1
Cf.
A007658 = numbers n such that (3^n + 1)/4 is prime. Cf.
A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf.
A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf.
A128066,
A128067,
A128068,
A128069,
A128070,
A128072,
A128073,
A128074,
A128075. Cf.
A059801 = numbers n such that 4^n - 3^n is prime. Cf.
A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf.
A128024,
A128025,
A128026,
A128027,
A128028,
A128029,
A128030,
A128031,
A128032.
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k=13; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
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is(n)=isprime((3^n+13^n)/16) \\ Charles R Greathouse IV, Feb 17 2017
A128075
Numbers k such that (3^k + 19^k)/22 is prime.
Original entry on oeis.org
3, 61, 71, 109, 9497, 36007, 50461, 66919
Offset: 1
Cf.
A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf.
A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf.
A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf.
A059801 (numbers k such that 4^k - 3^k is prime).
Cf.
A121877 (numbers k such that (5^k - 3^k)/2 is prime).
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k=19; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,9592} ]
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is(n)=isprime((3^n+19^n)/22) \\ Charles R Greathouse IV, Feb 17 2017
A128072
Numbers k such that (3^k + 14^k)/17 is prime.
Original entry on oeis.org
3, 7, 71, 251, 1429, 2131, 2689, 36683, 60763
Offset: 1
Cf.
A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf.
A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf.
A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf.
A059801 (numbers k such that 4^k - 3^k is prime).
Cf.
A121877 (numbers k such that (5^k - 3^k)/2 is prime).
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k=14; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
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is(n)=isprime((3^n+14^n)/17) \\ Charles R Greathouse IV, Feb 17 2017
A128073
Numbers k such that (3^k + 16^k)/19 is prime.
Original entry on oeis.org
5, 17, 61, 673, 919, 2089, 86939
Offset: 1
Cf.
A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf.
A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf.
A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf.
A059801 (numbers k such that 4^k - 3^k is prime).
Cf.
A121877 (numbers k such that (5^k - 3^k)/2 is prime).
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k=16; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
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is(n)=isprime((3^n+16^n)/19) \\ Charles R Greathouse IV, Feb 17 2017
A128067
Numbers k such that (3^k + 7^k)/10 is prime.
Original entry on oeis.org
3, 13, 31, 313, 3709, 7933, 14797, 30689, 38333
Offset: 1
Cf.
A007658 = numbers n such that (3^n + 1)/4 is prime. Cf.
A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf.
A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf.
A128066,
A128068,
A128069,
A128070,
A128071,
A128072,
A128073,
A128074,
A128075. Cf.
A059801 = numbers n such that 4^n - 3^n is prime. Cf.
A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf.
A128024,
A128025,
A128026,
A128027,
A128028,
A128029,
A128030,
A128031,
A128032.
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k=7; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
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is(n)=isprime((3^n+7^n)/10) \\ Charles R Greathouse IV, Feb 17 2017
A128070
Numbers k such that (3^k + 11^k)/14 is prime.
Original entry on oeis.org
3, 103, 271, 523, 23087, 69833
Offset: 1
Cf.
A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf.
A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf.
A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf.
A059801 (numbers k such that 4^k - 3^k is prime).
Cf.
A121877 (numbers k such that (5^k - 3^k)/2 is prime).
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k=11; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
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is(n)=isprime((3^n+11^n)/14) \\ Charles R Greathouse IV, Feb 17 2017
A128068
Numbers k such that (3^k + 8^k)/11 is prime.
Original entry on oeis.org
5, 163, 191, 229, 271, 733, 21059, 25237
Offset: 1
Cf.
A007658 = numbers n such that (3^n + 1)/4 is prime. Cf.
A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf.
A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf.
A128066,
A128067,
A128069,
A128070,
A128071,
A128072,
A128073,
A128074,
A128075. Cf.
A059801 = numbers n such that 4^n - 3^n is prime. Cf.
A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf.
A128024,
A128025,
A128026,
A128027,
A128028,
A128029,
A128030,
A128031,
A128032.
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k=8; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
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is(n)=isprime((3^n+8^n)/11) \\ Charles R Greathouse IV, Feb 17 2017
A328660
Numbers k such that (10^k + 7^k)/17 is prime.
Original entry on oeis.org
3, 5, 11, 19, 1259, 1399, 2539, 2843, 5857, 10589
Offset: 1
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[p: p in PrimesUpTo(1000) | IsPrime((10^p+7^p) div 17)]; // Modified by Jinyuan Wang, Jan 22 2020
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Select[Table[Prime[n], {n, 500}], PrimeQ[(10^#+7^#)/17] &] (* Modified by Jinyuan Wang, Jan 22 2020 *)
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forprime(k=3, 10000, if(isprime((10^k+7^k)/17), print1(k, ", ")))
Showing 1-9 of 9 results.
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