A054217 -id:A054217 - cp's OEIS frontend

A054218 Palindromic primes of the form 'primemirp' resulting from A054217.

2, 3, 5, 7, 131, 313, 373, 797, 11311, 17971, 18181, 19991, 35353, 72727, 78787, 90709, 93739, 96769, 98389, 1153511, 1193911, 1201021, 1409041, 1583851, 1597951, 1657561, 1831381, 1879781, 3083803, 3089803, 3319133, 3343433, 3391933, 3541453, 3643463

Offset: 1

Patrick De Geest, Feb 15 2000

Original idea from G. L. Honaker, Jr.

			Prime 113 has emirp 311 and 11311 is a palindromic prime.

Peter Rowlett, Table of n, a(n) for n = 1..8668

Cf. A054217, A000040, A006567, A048054, A002385.

from sympy import isprime
for i in range(2,10**7):
    if isprime(i):
        emirp = int(str(i)[-1::-1])
        if isprime(emirp):
            primemirp = int(str(i)+str(emirp)[1:])
            if isprime(primemirp):
                print(primemirp)
# Peter Rowlett, Nov 16 2023

a(33)-a(35) from Peter Rowlett, Nov 16 2023

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

A070954 Emirps which when concatenated with their reversals after a 0 make a palindromic prime of the form emirp0prime.

Original entry on oeis.org

31, 73, 149, 167, 347, 359, 769, 967, 1033, 1069, 1091, 1109, 1279, 1487, 1499, 1601, 1879, 1901, 1933, 3023, 3049, 3301, 3347, 3407, 3541, 3583, 3803, 3851, 3889, 7507, 7589, 7643, 7717, 7949, 9041, 9127, 9341, 9439, 9613, 9871, 10177, 10321, 10333

Offset: 1

Lekraj Beedassy, May 16 2002

			Emirp 359, for instance, generates the palprime 3590953.

Cf. A006567 and A054217.

Do[d = IntegerDigits[ Prime[n]]; If[ PrimeQ[ FromDigits[ Reverse[d]]] && PrimeQ[ FromDigits[ Join[d, {0}, Reverse[d]]]], Print[ Prime[n]]], {n, 1, 10^3}]

Corrected and extended by Robert G. Wilson v and Jason Earls, May 20 2002

A085777 Semiprimes such that when they are concatenated with their reversal are semiprime.

Original entry on oeis.org

14, 34, 38, 74, 91, 94, 115, 146, 169, 185, 194, 305, 334, 341, 346, 355, 361, 362, 386, 394, 395, 398, 706, 721, 731, 745, 755, 766, 794, 799, 901, 923, 926, 955, 974, 985, 1027, 1046, 1094, 1138, 1141, 1147, 1174, 1195, 1202, 1238, 1247, 1261, 1262, 1271

Offset: 1

Jason Earls, Jul 23 2003

This is to A001358 = semiprimes (or biprimes): products of two primes, as A054217 is to primes A000040. Note that a subsequence is the emirpimes (A097393) which, when concatenated with their digital reversals, become different semiprimes. Examples of this subsequence: 94, 115, 169, 185, ... because 9449 = 11 * 859, 115511 = 11 * 10501, 169961 = 11 * 15451, 185581 = 11 * 16871. [From Jonathan Vos Post, Apr 05 2010]

			a(7)=115 because 115511 = 11*10501.

Cf. A001358.

Cf. A000040, A001358, A004086, A097393 [From Jonathan Vos Post, Apr 05 2010]

{positive integers s = p*q in A001358, p and q primes, such that Concatenate(s, R(s)) = u*v is in A001358, u and v primes} = {positive integers s = p*q in A001358, p and q primes, such that Concatenate(s, A004086(s)) = u*v is in A001358, u and v primes}. [From Jonathan Vos Post, Apr 05 2010]

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A054218 Palindromic primes of the form 'primemirp' resulting from A054217.

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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.

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A070954 Emirps which when concatenated with their reversals after a 0 make a palindromic prime of the form emirp0prime.

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A085777 Semiprimes such that when they are concatenated with their reversal are semiprime.

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