A059661 Like A059459, but each term must be greater than the previous ones.

2, 3, 7, 23, 31, 4127, 4159, 20543, 134238271, 134238527, 167792959, 1241534783, 3389018431, 72108495167, 72108503359, 72108765503, 2722258935367507707706996859526254457151, 2722258935367507707708149781030861304127, 13611294676837538538536137218847444070719

Offset: 1

Author

Antti Karttunen, Feb 03 2001

Keywords

• nonn
• base

Links

• N. J. A. Sloane, Maple implementations of XORnos and DIFF

Crossrefs

Cf. A033875, A059459, A059662.

Programs

Maple

flip_primes_asc_search := proc(a,upto_bit,upto_length) local i,n,t; if(nops(a) >= upto_length) then RETURN(a); fi; t := a[nops(a)]; for i from 0 to upto_bit do n := XORnos(t,(2^i)); if(isprime(n) and (n > t)) then print([op(a), n]); RETURN(flip_primes_asc_search([op(a), n],upto_bit,upto_length)); fi; od; RETURN([op(a),`and no more`]); end;
flip_primes_asc_search([2],512,21);

Mathematica

uptobit = 512; uptolength = 17; Clear[f]; f[a_] := f[a] = Module[{n, i, t}, If[Length[a] >= uptolength, Return[a]]; t = a[[-1]]; For[i = 0, i <= uptobit, i++, n = BitXor[t, 2^i]; If[PrimeQ[n] && n > t, Return[f[Append[ a, n]]]]]]; A059661 = f[{2}] (* Jean-François Alcover, Mar 07 2016, adapted from Maple *)

Python

from sympy import isprime
from itertools import islice
def agen():
    an, bit = 2, 1
    while True:
        yield an
        while an&bit or not isprime(an+bit): bit <<= 1
        an += bit; bit = 1
print(list(islice(agen(), 17))) # Michael S. Branicky, Oct 01 2022

Formula

a(n) = 2 + Sum_{k=1..n-1} 2^A059662(k). - Pontus von Brömssen, Jan 07 2023