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 A239710 Primes of the form m = b^i + b^j + 1, where i > j > 0, b > 1. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 ----------- (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 Cf. A239708, A239709, A239711. Cf. A242100, A239712 - A239720. Sequence in context: A084467 A245179 A297177 * A227921 A176620 A059637 Adjacent sequences:  A239707 A239708 A239709 * A239711 A239712 A239713 KEYWORD nonn AUTHOR Hieronymus Fischer, Mar 27 2014 and May 04 2014 STATUS approved

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Last modified April 20 13:26 EDT 2021. Contains 343135 sequences. (Running on oeis4.)