A309574 n-th prime minus its ternary (base 3) reversal.

0, 2, -2, 2, -8, 0, -8, 8, 0, -26, -6, 6, -26, -6, -14, -26, -6, 14, 26, -6, 38, 26, -80, -128, -48, -80, -24, -128, 24, -80, 24, -80, -32, 24, -56, 0, 24, 80, -24, 0, -48, 80, 24, 80, -24, 104, 80, 80, 48, 104, 0, 24, 80, -398, -338, -278, -434, 18, -138

Offset

1,2

Comments

a(n) = 0 if and only if n is palindromic in base 3 - if and only if A000040(n) is in A014190.

As it occurs in its binary cousin, we observe that a scatter plot of this sequence shows parallelograms.

All terms are even. - Alois P. Heinz, Aug 08 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Samuel M. A. Luque, C++ Program (.cpp file) to generate this sequence in whichever m-th base you choose.

Samuel M. A. Luque, Scatter plot of a(n) up to n = 8132 (primes up to 50 000).

Formula

a(n) = A000040(n) - A030102(A000040(n)).

a(n) = A055947(A000040(n)).

Maple

a:= n-> (p-> p-(l->add(l[-i]*3^(i-1), i=1..nops(l))
        )(convert(p, base, 3)))(ithprime(n)):
seq(a(n), n=1..61);  # Alois P. Heinz, Aug 08 2019

Mathematica

(# - IntegerReverse[#, 3]) &@ Prime@ Range@ 60 (* Giovanni Resta, Aug 09 2019 *)

Prog

(Python)
from sympy import primerange
def rev(n, b):
    m = 0
    while n > 0:
        m, n = m*b+n%b, n//b
    return m
n, aa = 1, 1
while n <20:
    if aa in primerange(1, 200):
        print(n, aa-rev(aa, 3))
        n = n+1
    aa = aa+1 # A.H.M. Smeets, Aug 09 2019
(PARI) a(n) = my(p=prime(n)); p - fromdigits(Vecrev(digits(p, 3)), 3); \\ Michel Marcus, Aug 09 2019

Crossrefs

Cf. A000040, A014190, A030102, A055947, A265326.

Sequence in context: A367857 A121258 A087421 * A132697 A160689 A179976

Adjacent sequences: A309571 A309572 A309573 * A309575 A309576 A309577

Keyword

sign,base,look

Author

Samuel M. A. Luque Astorga, Aug 08 2019

Status

approved