A004087 -id:A004087 - cp's OEIS frontend

A135623 Mersenne primes written backwards.

3, 7, 13, 721, 1918, 170131, 782425, 7463847412, 1593963129003485032, 111265944731096246910079816, 721882010875193363312928672952261, 727501488517303786137132964064381141071

Offset: 1

Omar E. Pol, Feb 17 2008

			a(3)=13 because the 3rd Mersenne prime is 31.

Harvey P. Dale, Table of n, a(n) for n = 1..18
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000668, A004087.

IntegerReverse[2^MersennePrimeExponent[Range[15]]-1] (* Harvey P. Dale, Feb 26 2023 *)

A162706 Numbers that are the sum of two reversed primes.

Original entry on oeis.org

4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81

Offset: 1

Claudio Meller, Jul 11 2009

a(n) = A004087(j)+A004087(k) for any pair (j,k). - R. J. Mathar, Jul 13 2009

Edited, entries checked by R. J. Mathar, Jul 13 2009

A228355 Write the primes backwards in base 10 and juxtapose their digits.

Original entry on oeis.org

2, 3, 5, 7, 1, 1, 3, 1, 7, 1, 9, 1, 3, 2, 9, 2, 1, 3, 7, 3, 1, 4, 3, 4, 7, 4, 3, 5, 9, 5, 1, 6, 7, 6, 1, 7, 3, 7, 9, 7, 3, 8, 9, 8, 7, 9, 1, 0, 1, 3, 0, 1, 7, 0, 1, 9, 0, 1, 3, 1, 1, 7, 2, 1, 1, 3, 1, 7, 3, 1, 9, 3, 1, 9, 4, 1, 1, 5, 1, 7, 5, 1, 3, 6, 1, 7, 6

Offset: 0

Vincenzo Librandi, Aug 21 2013

Also, decimal expansion of the constant 0.235711317191329213731434743595...

The same sequence, but with different indexing, would arise for the table whose n-th row lists the A097944(n) digits of the n-th prime A000040(n) from right to left. - M. F. Hasler, Oct 24 2019

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Cf. A004087, A007376, A033308.

Reverse[IntegerDigits//@ Reverse@Prime@Range@50//Flatten]

fromdigits( A=concat(apply( row(n)=Vecrev(digits(prime(n))), [1..default(realprecision)])))*.1^#A \\ Result = the constant, A = sequence of digits, row(n) = n-th row of the table. - M. F. Hasler, Oct 24 2019

A072385 Primes which can be represented as the sum of a prime and its reverse.

Original entry on oeis.org

383, 443, 463, 787, 827, 887, 929, 1009, 1049, 1069, 1151, 1171, 1231, 1373, 1453, 1493, 1777, 30203, 30403, 31013, 32213, 32413, 32423, 33023, 33223, 34033, 34843, 35053, 36263, 36653, 37273, 37463, 37663, 38083, 38273, 38873, 39293, 39883

Offset: 1

Shyam Sunder Gupta, Jul 20 2002

This set is the image under the "reverse and add" operation (A056964) of the Luhn primes A061783 (which remain prime under that operation). Those have always an odd number of digits, and start with an even digit. Therefore this sequence has its terms in intervals [3,20]*100^k with k = 1, 2, 3.... - M. F. Hasler, Sep 26 2019

			383 is a term because it is prime and it is the sum of prime 241 and its reverse 142.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..253 from M. F. Hasler)
Matt Parker, 383 is cool, Numberphile series on YouTube, Feb. 15, 2017.

Cf. A004086 (reverse), A004087 (primes reversed), A056964 (reverse & add), A061783 (Luhn primes), A086002 (similar, using "rotate" instead of "reverse").

f@n_:=(Select[# + IntegerReverse[#] & /@ Prime[Range[n]], PrimeQ@# && # <= Prime[n] &] // Union); f@3000 (* Harvey P. Dale, Jul 18 2018; corrected by Hans Rudolf Widmer, Aug 15 2024 *)

is_A072385(p)={isprime(p)&&forprime(q=p\10,p*9\10,A056964(q)==p&&return(1))} \\ A056964(n)=n+fromdigits(Vecrev(digits(n))). It is much faster to produce the terms as shown below, rather than to "select" them from a range of primes. - M. F. Hasler, Sep 26 2019

A072385=Set(apply(A056964, A061783)) \\ with, e.g.: A061783=select(is_A061783(p)={isprime(A056964(p))&&isprime(p)}, primes(8713)) - M. F. Hasler, Sep 26 2019

a(n) = A056964(A061783(n)). - M. F. Hasler, Sep 26 2019

Cross-references added by M. F. Hasler, Sep 26 2019

A074895 Primes written backwards and sorted.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 14, 16, 17, 31, 32, 34, 35, 37, 38, 71, 73, 74, 76, 79, 91, 92, 95, 97, 98, 101, 104, 106, 107, 112, 113, 118, 119, 124, 125, 128, 131, 133, 134, 136, 142, 145, 146, 149, 151, 152, 157, 164, 166, 167, 172, 175, 179, 181, 182, 188, 191, 194

Offset: 1

Jason Earls, Sep 14 2002

Cf. A000040, A004087.

Take[Sort[FromDigits[Reverse[IntegerDigits[#]]]&/@Prime[Range[500]]],60] (* Harvey P. Dale, Nov 08 2011 *)
Take[Sort[IntegerReverse[Prime[Range[500]]]],60] (* Harvey P. Dale, Mar 26 2025 *)

Offset changed by Andrew Howroyd, Sep 18 2024

A104154 For each natural number n: if the last digit of n is not zero and A004086(n) is prime, append A004086(n) to the sequence.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 41, 61, 71, 13, 23, 43, 53, 73, 83, 17, 37, 47, 67, 97, 19, 29, 59, 79, 89, 101, 401, 601, 701, 211, 311, 811, 911, 421, 521, 821, 131, 331, 431, 631, 241, 541, 641, 941, 151, 251, 751, 461, 661, 761, 271, 571, 971, 181, 281, 881

Offset: 1

Cino Hilliard, Mar 09 2005

Equivalently, these are the prime numbers ordered by their reversal. - Rémy Sigrist, Feb 13 2022

			The last digit of 13 is not '0' and 31 is prime, therefore we append 31.

Rémy Sigrist, Table of n, a(n) for n = 1..9592

Cf. A004087.

a = Select[Range[196], IntegerDigits[ # ][[ -1]] != 0 && PrimeQ[FromDigits[Reverse[ IntegerDigits[ # ]]]] &]; b = {}; For[n = 1, n < Length[a] + 1, n++, AppendTo[b, FromDigits[Reverse[IntegerDigits[a[[n]]]]]]]; b

left(str, n) = { my(v, tmp, x); v =""; tmp = Vec(str); ln=length(tmp); if(n > ln, n=ln); for(x=1, n, v=concat(v, tmp[x]); ); return(v) } \\ Get the left n characters from string str
rev(str) = { local(tmp, s, j); tmp = Vec(Str(str)); s=""; forstep(j=length(tmp), 1, -1, s=concat(s, tmp[j])); return(s) } \\ Get the reverse of the input string
rprime(n) = { local(x, y, v); for(x=1, n, y=rev(x); v=Vec(y); if(left(y, 1)<> "0"&&isprime(eval(y)), print1(y", ")) ) }

from itertools import count, islice
from sympy import primerange
def A104154_gen(): # generator of terms
    yield from (int(d[::-1]) for l in count(1) for d in sorted(str(m)[::-1] for m in primerange(10**(l-1),10**l)))
A104154_list = list(islice(A104154_gen(),20)) # Chai Wah Wu, Feb 17 2022

Edited by Stefan Steinerberger, Aug 01 2007

A232446 Primes p such that reversal( p^2 ) + p is also prime.

Original entry on oeis.org

7, 151, 787, 1549, 1579, 2029, 2083, 2179, 2833, 2971, 4549, 4591, 4801, 4999, 5077, 5167, 5179, 5209, 5227, 5407, 6343, 6529, 6547, 6553, 6577, 6679, 7027, 7753, 7867, 7873, 7927, 7963, 7993, 8167, 8191, 8311, 9091, 9103, 9151, 9283, 14251, 14281, 14389, 14437

Offset: 1

K. D. Bajpai, Nov 24 2013

nonn

			a(1)= 7, it is prime: prime(4)= 7: reversal(7^2)+7= reversal(49)+7= 94+7= 101 which is also prime.
a(2)= 151, it is prime: prime(36)= 151: reversal(151^2)+151= reversal(22801)+151=10822+151= 10973 which is also prime.

K. D. Bajpai, Table of n, a(n) for n = 1..4250

Cf. A061783 (primes p: p+(p reversed) is also prime).

Function reversal is given by A004086. Cf. also A004087.

with(StringTools): KD:= proc() local a,p; p:=ithprime(n);a:= parse(Reverse(convert((p^2), string)))+p; if isprime(a) then RETURN (p): fi; end: seq(KD(), n=1..3000);

Select[Prime[Range[3000]], PrimeQ[# + FromDigits[Reverse[IntegerDigits[#^2]]]] &]

A062018 a(n) = n^n written backwards.

Original entry on oeis.org

1, 4, 72, 652, 5213, 65664, 345328, 61277761, 984024783, 1, 116076113582, 6528440016198, 352295601578203, 61085552860021111, 573958083098398734, 61615590737044764481, 771467633688162042728, 42457573569257080464393

Offset: 1

Amarnath Murthy, Jun 01 2001

			a(5) = 5213, as 5^5 = 3125.

Harry J. Smith, Table of n, a(n) for n = 1..200

Cf. A004086, A004093, A004156, A034906, A004094, A004167, A002108, A002118, A002138, A002140, A002232, A002239, A002241, A002942, A004165, A004087, A004091, A004096, A004098, A004150, A004153.

with(numtheory):for n from 1 to 50 do a := convert(n^n,base,10):b := add(10^(nops(a)- i)*a[i],i=1..nops(a)):printf(`%d,`,b); od:

Table[IntegerReverse[n^n],{n,20}] (* Harvey P. Dale, Jul 31 2022 *)

a(n) = { fromdigits(Vecrev(digits( n^n )))} \\ Harry J. Smith, Jul 29 2009

a(n) = A004086(n^n).

More terms from Jason Earls and Vladeta Jovovic, Jun 01 2001

A098922 Reverse digits of largest primes, append to sequence if result is larger prime then previous one with reverse digits.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 71, 73, 97, 101, 701, 941, 971, 991, 9001, 9601, 9721, 9931, 9941, 9967, 70001, 90001, 93001, 96001, 97001, 99401, 99611, 99721, 99881, 99923, 99989, 940001, 972001, 973001, 996001, 997001, 999101, 999331, 999431, 999631, 999931

Offset: 1

Jani Melik, Oct 18 2004

			The prime 37 in reverse is 73. 73 is prime and is larger than previous prime (17), written with reverse digits 71.

Cf. A004087, A095180.

obrni_stev:=proc(n) local i, tren, tren1, st, ans; ans:=[ ]: tren:=n: tren1:=0: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): od; for i from 0 to nops(ans)-1 do tren1:= tren1 + op(nops(ans)-i, ans)*10^(i); od: RETURN(tren1); end: ts_inv_prav_pra:= proc(n) local i, tren, ans; tren:=0: ans:=[ ]: for i from 1 to n do if ( isprime( i ) = 'true' and isprime( obrni_stev (i) )='true' and obrni_stev(i) > tren ) then ans:=[ op(ans),obrni_stev(i) ]; tren:=obrni_stev(i); fi: od: RETURN(ans); end: ts_inv_prav_pra(200000);

A103163 a(n) = gcd(reverse(prime(n)), reverse(prime(n+1))).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 5, 1, 4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 14, 2, 2, 2, 4, 2, 2, 8, 2, 2, 2, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 8, 2, 2, 2, 2, 2, 2, 8, 2, 2, 4, 4, 2, 2, 2, 2, 1, 5, 5, 25, 5, 5, 5, 5, 5, 5, 25, 5, 5, 5, 1, 2, 2, 4, 4, 4

Offset: 1

Labos Elemer, Jan 27 2005

Greatest common divisor of two consecutive primes after each prime is written backward.

			Neither of these common divisors are divisible by 3 or by 10 or by 11.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A004087, A000040.

A103163 := proc(n)
    p := ithprime(n) ;
    q := nextprime(p) ;
    igcd(digrev(p),digrev(q)) ;
end proc:
seq(A103163(n),n=1..114) ; # R. J. Mathar, Sep 22 2018

rd[x_] :=FromDigits[Reversed[IntegerDigits[x]]]; Table[GCD[rd[Prime[w]], rd[Prime[w+1]]], {w, 1, 1000}]
GCD@@#&/@(Partition[IntegerReverse/@Prime[Range[120]],2,1]) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 31 2020 *)

a(n) = gcd(A004087(n), A004087(n+1)).

Edited by Jon E. Schoenfield, Oct 26 2019

cp's OEIS Frontend

A135623 Mersenne primes written backwards.

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A162706 Numbers that are the sum of two reversed primes.

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A228355 Write the primes backwards in base 10 and juxtapose their digits.

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A072385 Primes which can be represented as the sum of a prime and its reverse.

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PARI

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A074895 Primes written backwards and sorted.

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A104154 For each natural number n: if the last digit of n is not zero and A004086(n) is prime, append A004086(n) to the sequence.

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A232446 Primes p such that reversal( p^2 ) + p is also prime.

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Maple

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A062018 a(n) = n^n written backwards.

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Maple