A054218 -id:A054218 - cp's OEIS frontend

A054217 Primes p with property that p concatenated with its emirp p' (prime reversal) forms a palindromic prime of the form 'primemirp' (rightmost digit of p and leftmost digit of p' are blended together - p and p' palindromic allowed).

2, 3, 5, 7, 13, 31, 37, 79, 113, 179, 181, 199, 353, 727, 787, 907, 937, 967, 983, 1153, 1193, 1201, 1409, 1583, 1597, 1657, 1831, 1879, 3083, 3089, 3319, 3343, 3391, 3541, 3643, 3853, 7057, 7177, 7507, 7681, 7867, 7949, 9103, 9127, 9173, 9209, 9439, 9547, 9601

Offset: 1

Patrick De Geest, Feb 15 2000

Original idea from G. L. Honaker, Jr..

			E.g., prime 113 has emirp 311 and 11311 is a palindromic prime, so 113 is a term.

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A054218, A000040, A006567, A048054, A002385.

empQ[n_]:=Module[{idn=IntegerDigits[n],rev},rev=Reverse[idn];And@@PrimeQ[ {FromDigits[ rev],FromDigits[Join[Most[idn],rev]]}]]; Select[Prime[ Range[ 1200]],empQ] (* Harvey P. Dale, Mar 26 2013 *)

from sympy import isprime
def ok(n):
    if not isprime(n): return False
    s = str(n); srev = s[::-1]
    return isprime(int(srev)) and isprime(int(s[:-1] + srev))
print([k for k in range(10**4) if ok(k)]) # Michael S. Branicky, Nov 17 2023

Corrected (a(30)=3089 inserted) by Harvey P. Dale, Mar 26 2013

A258084 Numbers n such that n concatenated with its reversal n' yields a prime when the rightmost digit of n and leftmost digit of n' are coalesced.

Original entry on oeis.org

2, 3, 5, 7, 10, 13, 15, 18, 19, 31, 35, 37, 38, 72, 75, 78, 79, 91, 92, 100, 103, 105, 106, 113, 114, 124, 127, 128, 133, 138, 139, 143, 147, 154, 155, 163, 165, 166, 174, 179, 181, 184, 193, 198, 199, 301, 302, 304, 307, 308, 315, 323, 324, 335, 345, 348, 351

Offset: 1

K. D. Bajpai, May 19 2015

Alternatively, numbers n such that if n is concatenated with its reversal n', blending together the rightmost digit of n and the leftmost digit of n' yields a prime.
Leading zeros of n’ are discarded. For example, with 100, the reversal is 001; discarding its leading zeros gives 1; since the rightmost digit of 100 does not coincide with the leftmost digit 1 of n’, discard the rightmost digit of 100 - that results in the concatenated number 101, which is prime.
All the terms in this sequence will generate (probably) palindromic primes.

			a(6) = 13: Reversal of its digits gives 31. Concatenating 13 with 31, blending together 3's, results in 131, which is prime.
a(26) = 124: Reversal of its digits gives 421. Concatenating 124 with 421, blending together 4's, results in 12421, which is prime.

K. D. Bajpai, Table of n, a(n) for n = 1..5493

Cf. A000040, A004086, A054217, A054218.

Select[Range[1, 1200], PrimeQ[FromDigits[Join[IntegerDigits [FromDigits [Join[Most [IntegerDigits[#]]]]], IntegerDigits[FromDigits [Reverse[IntegerDigits[#]]]]]] ] &]

for(n=1,200,d=digits(n);m=(10^#d)*floor(n/10);s=sum(i=1,#d,d[i]*10^(i-1));if(isprime(m+s),print1(n,", "))) \\ Derek Orr, Jun 22 2015

cp's OEIS Frontend

A054217 Primes p with property that p concatenated with its emirp p' (prime reversal) forms a palindromic prime of the form 'primemirp' (rightmost digit of p and leftmost digit of p' are blended together - p and p' palindromic allowed).

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