A122261 Characteristic function of numbers having only factors that are Pierpont primes.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..12289

Eric Weisstein's World of Mathematics, Pierpont Prime

Index entries for characteristic functions

Formula

Multiplicative with a(p) = A065333(p-1), for p prime.

a(n) = if n=1 then 0 else A122262(n) - A122262(n-1).

a(A122260(n)) = 1.

a(n) = A122255(n) for n < 25.

Example

For n = 11 = 11^1, 11 is not a Pierpoint prime because 11-1 = 10 = 2*5 has a prime factor larger than 3, thus a(11) = 0.
For n = 25 = 5^2, 5 is a Pierpoint prime as 5-1 = 4 = 2^2 does not have any prime factors larger than 3, thus a(25) = 1.

Mathematica

Block[{nn = 105, s}, s = Select[Sort@ Flatten@ Table[2^i*3^j + 1, {i, 0, Log2@ nn}, {j, 0, Log[3, nn/2^i]}] , PrimeQ]; Table[Boole[n == 1] + Boole@ AllTrue[FactorInteger[n][[All, 1]], MemberQ[s, #] &], {n, nn}]] (* Michael De Vlieger, Aug 23 2017, after Robert G. Wilson v at A005109 *)

Prog

(PARI)
A065333(n) = ((3^valuation(n, 3)<<valuation(n, 2))==n); \\ This function from Charles R Greathouse IV, Aug 21 2011
A122261(n) = factorback(apply(p -> A065333(p-1), (factor(n)[, 1]))); \\ Antti Karttunen, Aug 22 2017

Crossrefs

Cf. A005109, A065333, A122255, A122262 (partial sums).

Characteristic function of A122260.

Sequence in context: A225595 A228813 A122255 * A015120 A015142 A015186

Adjacent sequences: A122258 A122259 A122260 * A122262 A122263 A122264

Keyword

nonn,mult

Author

Reinhard Zumkeller, Aug 29 2006

Extensions

An unnecessary part removed from the formula and the Example section added by Antti Karttunen, Aug 22 2017

Status

approved