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A128066
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Numbers n such that (3^n + 4^n)/7 is prime.
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8
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3, 5, 19, 37, 173, 211, 227, 619, 977, 1237, 2437, 5741, 13463, 23929, 81223, 121271
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All terms are primes.
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LINKS
| Top probable primes of the form (4^p+3^p)/7
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MAPLE
| 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 (deutsch(AT)duke.poly.edu), Feb 17 2007
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MATHEMATICA
| Do[ p=Prime[n]; f=(3^p+4^p)/(4+3); If[ PrimeQ[f], Print[p]], {n, 1, 100} ]
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PROG
| (PARI) f(n)=(3^n + 4^n)/7;
forprime(n=3, 10^5, if(ispseudoprime(f(n)), print1(n, ", ")))
/* Joerg Arndt, Mar 27 2011 */
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CROSSREFS
| Cf. A007658 = n such that (3^n + 1)/4 is prime; A057469 ((3^n + 2^n)/5); A122853 ((3^n + 5^n)/8).
Cf. A128067, A128068, A128069, A128070, A128071, A128072, A128073, A128074, A128075.
Cf. A059801 (4^n - 3^n); A121877 ((5^n - 3^n)/2).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
Sequence in context: A068990 A062594 A128027 * A148523 A148524 A148525
Adjacent sequences: A128063 A128064 A128065 * A128067 A128068 A128069
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KEYWORD
| hard,more,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 14 2007
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EXTENSIONS
| 3 more terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 17 2007
2 more terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Apr 16 2007
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 (chartonjl(AT)wanadoo.fr), 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
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