A074832 -id:A074832 - cp's OEIS frontend

A366910 Number of n-bit binary reversible primes.

0, 1, 2, 2, 4, 6, 9, 14, 27, 36, 69, 94, 178, 308, 589, 908, 1540, 2814, 5158, 9210, 16732, 29392, 55109, 101120, 179654, 332130, 625928, 1136814, 2120399, 3963166, 7377931, 13878622, 25958590, 48421044, 92163237, 173672988, 325098134, 617741968, 1177573074, 2221353224, 4222570054

Offset: 1

Cathy Swaenepoel, Oct 27 2023

Number of primes p in [2^(n-1),2^n) whose reverse in base 2 is also prime. The count includes palindromic primes in base 2.

			The 5-bit binary reversible primes are 17="10001", 23="10111", 29="11101" and 31="11111", so a(5)=4.

Cathy Swaenepoel, Table of n, a(n) for n = 1..50
Cécile Dartyge, Bruno Martin, Joël Rivat, Igor E. Shparlinski, and Cathy Swaenepoel, Reversible primes, arXiv:2309.11380 [math.NT], 2023. See p. 34.

Cf. A074831, A074832, A117773, A048054.

A377421 Numbers whose binary reversal is prime and unequal to the original number.

Original entry on oeis.org

6, 10, 11, 12, 13, 14, 20, 22, 23, 24, 25, 26, 28, 29, 34, 37, 40, 41, 43, 44, 46, 47, 48, 50, 52, 53, 55, 56, 58, 61, 62, 67, 68, 71, 74, 77, 80, 82, 83, 86, 88, 91, 92, 94, 96, 97, 100, 101, 104, 106, 110, 112, 113, 115, 116, 121, 122, 124, 131, 134, 136, 142

Offset: 1

Simon R Blow, Oct 27 2024

Contains A080790 and p*2^i for all primes p in A074832 union A080790 and i > 0. - Michael S. Branicky, Oct 29 2024

			6 = 110_2 is a term since reversed it is 011_2 = 3 which is prime.
7 = 111_2 is not a term since base 2 palindromic numbers are not included.

James C. McMahon, Table of n, a(n) for n = 1..10000

Supersequence of A080790.

Cf. A030101, A006995, A074832, A204232.

Select[Range[142],PrimeQ[r=FromDigits[Reverse[IntegerDigits[#,2]],2]]&&r!=#&] (* James C. McMahon, Nov 18 2024 *)

from sympy import isprime
def ok(n): return (b:=bin(n)[2:]) != (br:=b[::-1]) and isprime(int(br, 2))
print([k for k in range(1, 143) if ok(k)]) # Michael S. Branicky, Oct 28 2024

# alternate program constructing terms directly from primes
from sympy import primerange
def auptobits(maxbits):
    alst = []
    for p in primerange(3, 1<Michael S. Branicky, Oct 29 2024

a = A204232 - A006995 (as sets). - Michael S. Branicky, Oct 29 2024

A226035 Prime powers (A025475) whose decimal digit reversal is also a prime power.

Original entry on oeis.org

1, 4, 8, 9, 121, 169, 343, 961, 1331, 10201, 12769, 14641, 94249, 96721, 1030301, 1042441, 1062961, 1216609, 1442401, 1692601, 9066121, 104060401, 121066009, 900660121, 12148668841, 12367886521, 12568876321, 14886684121, 1000422044521, 1002007006009, 1020506060401

Offset: 1

Alex Ratushnyak, May 24 2013

Cf. A025475, A007500, A061455, A074832.

cp's OEIS Frontend

A366910 Number of n-bit binary reversible primes.

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A377421 Numbers whose binary reversal is prime and unequal to the original number.

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A226035 Prime powers (A025475) whose decimal digit reversal is also a prime power.

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