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

1,1

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

Cf. A033875, A059459, A059662.

Sequence in context: A278477 A118883 A061712 * A214704 A231075 A072686

Adjacent sequences: A059658 A059659 A059660 * A059662 A059663 A059664

Keyword

nonn,base

Author

Antti Karttunen, Feb 03 2001

Status

approved