A059661 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..19.

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

FORMULA

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

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 *)

PROG

(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

CROSSREFS