A239710 Primes of the form m = b^i + b^j + 1, where i > j > 0, b > 1.
7, 11, 13, 19, 31, 37, 41, 43, 67, 73, 97, 109, 131, 137, 151, 157, 193, 211, 223, 241, 271, 307, 421, 463, 521, 577, 601, 631, 641, 733, 739, 751, 757, 769, 811, 1033, 1123, 1153, 1303, 1453, 1483, 1723, 1741, 1873, 2053, 2081, 2113, 2269, 2551, 2917, 2971, 3251, 3307, 3391, 3541, 3907, 4099
Offset: 1
Keywords
Examples
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.
Links
- Hieronymus Fischer, Table of n, a(n) for n = 1..10000
Programs
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Smalltalk
A239710 "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]
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