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 A272892 Taxi-cab numbers n such that n-1 and n+1 are both prime. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..6385 a(n) for n = 1..88 from Charles R Greathouse IV EXAMPLE Taxi-cab number 32832 is a term because 32831 and 32833 are twin primes. PROG (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 CROSSREFS Cf. A001235, A014574. Sequence in context: A168634 A045061 A183889 * A230524 A168666 A353019 Adjacent sequences: A272889 A272890 A272891 * A272893 A272894 A272895 KEYWORD nonn AUTHOR Altug Alkan, May 09 2016 EXTENSIONS a(7)-a(25) from Charles R Greathouse IV, May 09 2016 STATUS approved

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Last modified May 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)