A076055 -id:A076055 - cp's OEIS frontend

A095179 Numbers whose reversed digit representation is prime.

2, 3, 5, 7, 11, 13, 14, 16, 17, 20, 30, 31, 32, 34, 35, 37, 38, 50, 70, 71, 73, 74, 76, 79, 91, 92, 95, 97, 98, 101, 104, 106, 107, 110, 112, 113, 118, 119, 124, 125, 128, 130, 131, 133, 134, 136, 140, 142, 145, 146, 149, 151, 152, 157, 160, 164, 166, 167, 170, 172

Offset: 1

Cino Hilliard, Jun 21 2004

If m is a term, then 10*m is another term. - Bernard Schott, Nov 20 2021

			The number 70 in reverse is 07 = 7, which is prime.

Michael S. Branicky, Table of n, a(n) for n = 1..11018 (all terms < 10**5)

Cf. A004086, A007500 (primes in this sequence), A076055 (composites in this sequence), A204232 (base-2 analog), A097312.

q:= n-> (s-> isprime(parse(cat(s[-i]$i=1..length(s)))))(""||n):
select(q, [$1..200])[];  # Alois P. Heinz, Aug 22 2021

Select[Range[200], PrimeQ[FromDigits[Reverse[IntegerDigits[#]]]] &] (* Harvey P. Dale, Jun 13 2013 *)

r(n) = for(x=1,n,y=eval(rev(x));if(isprime(y),print1(x","))) \ Get the reverse of the input string rev(str) = { local(tmp,j,s); tmp = Vec(Str(str)); s=""; forstep(j=length(tmp),1,-1, s=concat(s,tmp[j])); return(s) }

is_A095179(n)=isprime(eval(Strchr(vecextract(Vec(Vecsmall(Str(n))),"-1..1")))) \\ M. F. Hasler, Jan 13 2012

isok(n) = isprime(fromdigits(Vecrev(digits(n)))); \\ Michel Marcus, Aug 22 2021

from sympy import isprime
def ok(n): return isprime(int(str(n)[::-1]))
print(list(filter(ok, range(1, 173)))) # Michael S. Branicky, Aug 22 2021

Offset corrected to 1 by Alonso del Arte, Apr 12 2020

A076056 Primes which when read backwards are composite numbers.

Original entry on oeis.org

19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 103, 109, 127, 137, 139, 163, 173, 193, 197, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 317, 331, 349, 367, 379, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457

Offset: 1

Amarnath Murthy, Oct 04 2002

Subsidiary sequences that could be added:(1) Start of the first occurrence of n consecutive primes in the above sequence. (2) Start of the first occurrence of n consecutive primes with digit reversal also a prime.
The subsidiary sequence (1) with the indices at which n>=2 consecutive primes are first found in this sequence is 1, 1, 4, 4, 4, 4, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, ... - R. J. Mathar, May 22 2009
Subsequence of A151768. - Reinhard Zumkeller, Jul 06 2009

Anders Hellström, Table of n, a(n) for n = 1..10000
Anders Hellström, Sage program

Cf. A076055.

Complement of A007500 with respect to A000040. [From Reinhard Zumkeller, Jul 06 2009]

[p: p in PrimesUpTo(500)|not IsPrime(Seqint(Reverse(Intseq(p))))]; // Vincenzo Librandi, Jun 03 2019

Select[Prime[Range[100]], !PrimeQ[FromDigits[Reverse[IntegerDigits[ # ]]]]&]

More terms from Harvey P. Dale, Oct 11 2002

A224400 Composite numbers that become prime when their digits are put in nondecreasing order.

Original entry on oeis.org

20, 30, 32, 50, 70, 74, 76, 91, 92, 95, 98, 110, 130, 170, 172, 175, 176, 190, 194, 200, 203, 209, 217, 230, 232, 272, 275, 290, 292, 296, 300, 301, 302, 310, 319, 320, 322, 323, 329, 332, 370, 371, 374, 376, 391, 392, 394, 395, 398, 407, 437, 470, 473, 475

Offset: 1

Christian N. K. Anderson and Kevin L. Schwartz, Apr 05 2013

Conjecture: a(n) ~ 7.75*n.

			217 = 7*31, but 127 is prime. 302 = 2*151, but 23 is prime.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Subset of A007935.

Cf. A068653, A076055, A224402.

Select[Range[500], ! PrimeQ[#] && PrimeQ[FromDigits[Sort[IntegerDigits[#]]]] &] (* T. D. Noe, Apr 05 2013 *)

j=1; y=c(); library(gmp)
while(length(y)<1000) {
if(isprime((j=j+1))==0) {
x=sort(as.numeric(strsplit(as.character(j),spl="")[[1]]))
if(isprime(paste(x[x>0],collapse=""))>0) y=c(y,j) #drop leading zeros
}
}

A224402 Composite numbers that become prime when their digits are put in nonincreasing order.

Original entry on oeis.org

14, 16, 34, 35, 38, 112, 118, 119, 121, 124, 125, 128, 133, 134, 136, 142, 143, 145, 146, 152, 154, 164, 166, 175, 176, 182, 188, 194, 214, 215, 218, 314, 316, 334, 341, 343, 344, 346, 356, 358, 361, 364, 365, 368, 374, 377, 385, 386, 388, 395, 398, 412, 413

Offset: 1

Christian N. K. Anderson and Kevin L. Schwartz, Apr 05 2013

Because any number ending in zero is composite, the sequence experiences gaps of at least order O(a(n))-1 between changes in the most significant digit.

			194=2*97, but 941 is prime.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Subset of A007935.

Cf. A068653, A076055, A224400.

Select[Range[500], ! PrimeQ[#] && PrimeQ[FromDigits[Reverse[Sort[IntegerDigits[#]]]]] &] (* T. D. Noe, Apr 05 2013 *)

j=1; y=c(); library(gmp)
while(length(y)<1000) {
if(isprime((j=j+1))==0) {
x=sort(as.numeric(strsplit(as.character(j),spl="")[[1]]),decr=T)
if(isprime(paste(x,collapse=""))>0) y=c(y,j)
}
}

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A095179 Numbers whose reversed digit representation is prime.

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A076056 Primes which when read backwards are composite numbers.

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Magma

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A224400 Composite numbers that become prime when their digits are put in nondecreasing order.

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Mathematica

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A224402 Composite numbers that become prime when their digits are put in nonincreasing order.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

R