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A272892
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Taxi-cab numbers n such that n-1 and n+1 are both prime.
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1
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32832, 513000, 2101248, 8647128, 43570872, 46661832, 152275032, 166383000, 175959000, 351981000, 543449088, 610991208, 809557632, 970168752, 1710972648, 2250265752, 2262814272, 2560837032, 3222013032, 3308144112, 3582836712, 4505949000, 4543936488, 4674301632, 4868489178
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OFFSET
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1,1
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COMMENTS
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Taxi-cab numbers that are in A014574.
There are two versions of "taxicab numbers" that are A001235 and A011541. This sequence focuses on the version A001235.
First six terms are 2^6*3^3*19, 2^3*3^3*5^3*19, 2^12*3^3*19, 2^3*3^3*7^2*19*43, 2^3*3^6*31*241, 2^3*3^8*7*127.
This sequence contains many terms that are divisible by 6^3 = 216. But there are also terms that are not divisible by 6^3. For example, 166383*10^3 and 351981*10^3 are terms that are not divisible by 216.
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LINKS
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EXAMPLE
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Taxi-cab number 32832 is a term because 32831 and 32833 are twin primes.
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PROG
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(PARI) T=thueinit(x^3+1, 1);
isA001235(n)=my(v=thue(T, n)); sum(i=1, #v, v[i][1]>=0 && v[i][2]>=v[i][1])>1
p=2; forprime(q=3, 1e9, if(q-p==2 && isA001235(p+1), print1(p+1", ")); p=q) \\ Charles R Greathouse IV, May 09 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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