OFFSET
1,1
COMMENTS
If m is a term, then there is a base b > 1 such that the base-b representation of m has digital sum = 3.
The base b for which m = b^i + b^j + 1 is not uniquely determined. Example: 13 = 2^3+2^2+1 = 3^2 +3^1+1.
Numbers m that satisfy m = b^i + b^j + 1 and b == 1 (mod 3) are not terms.
LINKS
Hieronymus Fischer, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 7, since 7 = 2^2 + 2^1 + 1 is prime.
a(2) = 11, since 11 = 2^3 + 2^1 + 1 is prime.
a(5) = 31, since 31 = 3^3 + 3^1 + 1 is prime.
a(10) = 73.
a(100) = 24181.
a(10^3) = 23160157.
a(10^4) = 7039461703.
a(10^5) = 1226630453623.
a(10^6) = 182489744292253.
PROG
(Smalltalk)
"Answers the n-th term of A239710.
Usage: n A239710
Answer: a(n)"
^(self primesWhichAreDistinctPowersWithOffset: 1) at: self
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(Smalltalk)
primesWhichAreDistinctPowersWithOffset: d
"Answers an array which hold the first n primes of the form b^i + b^j + d, i>j>0, where n is the receiver. Iterative calculation, b > 1.
Usage: n primesWhichAreDistinctPowersWithOffset: d
Answer: all terms < n"
| n terms m |
terms := OrderedCollection new.
n := self.
m := n squared * (n integerCeilLog: 2) * 2.
terms := m primesLTnWhichAreDistinctPowersWithOffset: d.
[terms size < n] whileTrue:
[m := 2 * m.
terms := m primesLTnWhichAreDistinctPowersWithOffset: d].
^(terms copyFrom: 1 to: n) asArray
-----------
(Smalltalk)
primesLTnWhichAreDistinctPowersWithOffset: d
"Answers an array which hold the primes < n of the form b^i + b^j + d, i>j>0, where n is the receiver, b > 1.
Uses floorDistinctPowersWithOffset: d from A242100"
^(self floorDistinctPowersWithOffset: d) select: [:i | i isPrime]
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Mar 27 2014 and May 04 2014
STATUS
approved