A272892 - OEIS

A272892

Taxi-cab numbers n such that n-1 and n+1 are both prime.

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

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