A087766 -id:A087766 - cp's OEIS frontend

A087762 Primes whose reversal is a multiple of 7.

7, 19, 41, 53, 89, 103, 127, 139, 173, 197, 211, 223, 281, 293, 331, 367, 379, 463, 487, 499, 571, 691, 719, 827, 839, 911, 947, 1013, 1049, 1277, 1289, 1303, 1327, 1361, 1373, 1423, 1447, 1459, 1481, 1493, 1531, 1543, 1567, 1579, 1663, 1699, 1783, 1907

Offset: 1

Zak Seidov, Oct 03 2003

Mohammed Yaseen, Table of n, a(n) for n = 1..10000

Primes whose reversal is a multiple of k: this sequence (k=7), A087764 (k=13), A087765 (k=17), A087766 (k=19), A087767 (k=23).

Select[Prime[Range[300]],Divisible[FromDigits[Reverse[IntegerDigits[ #]]], 7]&] (* Harvey P. Dale, Dec 05 2012 *)

forprime(n=2, 2000, if(fromdigits(Vecrev(digits(n)))%7==0, print1(n, ", "))) \\ Mohammed Yaseen, Jul 19 2022

A087764 Primes whose reversal is a multiple of 13.

Original entry on oeis.org

19, 31, 269, 281, 397, 401, 457, 463, 523, 773, 827, 1063, 1117, 1123, 1367, 1373, 1427, 1433, 1489, 1549, 1609, 1621, 1871, 1931, 1987, 1993, 2027, 2089, 2161, 2221, 2399, 2459, 2531, 2593, 2647, 2707, 2713

Offset: 1

Zak Seidov, Oct 03 2003

There are no primes (besides 11) whose reversal is a multiple of 11.

Robert Israel, Table of n, a(n) for n = 1..10000

Primes whose reversal is a multiple of k: A087762 (k=7), this sequence (k=13), A087765 (k=17), A087766 (k=19), A087767 (k=23).

digrev:= proc(n) local L, i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
B:= map(digrev, {seq(i,i=13..10000,13)}):
sort(convert(select(isprime, B),list)); # Robert Israel, Oct 23 2019

forprime(n=2, 3000, if(fromdigits(Vecrev(digits(n)))%13==0, print1(n, ", "))) \\ Mohammed Yaseen, Jul 19 2022

A087765 Primes whose reversal is a multiple of 17.

Original entry on oeis.org

43, 71, 109, 137, 193, 631, 911, 997, 1049, 1291, 1543, 1571, 1609, 1637, 1693, 1759, 1787, 1823, 1973, 2053, 2081, 2269, 2297, 2333, 2549, 2699, 2707, 2791, 2857, 3001, 3217, 3581, 3769, 3797, 3833, 4007, 4091, 4129, 4157, 4409, 4493, 4651, 4903, 4931, 5011

Offset: 1

Zak Seidov, Oct 03 2003

Mohammed Yaseen, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Primes whose reversal is a multiple of k: A045711 (k=5), A087762 (k=7), A087764 (k=13), this sequence (k=17), A087766 (k=19), A087767 (k=23).

Select[Prime[Range[700]],Divisible[IntegerReverse[#],17]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 25 2019 *)

forprime(n=2, 6000, if(fromdigits(Vecrev(digits(n)))%17==0, print1(n, ", "))) \\ Mohammed Yaseen, Jul 20 2022

Corrected and extended by Ray Chandler, Oct 05 2003

Corrected and extended by Harvey P. Dale, Aug 25 2019

A087767 Primes whose reversal is a multiple of 23.

Original entry on oeis.org

29, 193, 223, 317, 349, 863, 1163, 1289, 1319, 1451, 1483, 1607, 1801, 2579, 2609, 2741, 2803, 3041, 3167, 3229, 3361, 3517, 4363, 4457, 4519, 4651, 5077, 5107, 5333, 5591, 5653, 5779, 6047, 6079, 6367, 6911, 7211, 7243, 7369, 7883

Offset: 1

Zak Seidov, Oct 03 2003

Mohammed Yaseen, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Primes whose reversal is a multiple of k: A045711 (k=5), A087762 (k=7), A087764 (k=13), A087765 (k=17), A087766 (k=19), this sequence (k=23).

Select[Prime[Range[1000]],Divisible[IntegerReverse[#],23]&] (* Harvey P. Dale, Apr 22 2022 *)

forprime(n=2, 8000, if(fromdigits(Vecrev(digits(n)))%23==0, print1(n, ", "))) \\ Mohammed Yaseen, Jul 20 2022

A355430 Primes starting with an even decimal digit.

Original entry on oeis.org

2, 23, 29, 41, 43, 47, 61, 67, 83, 89, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 809, 811, 821

Offset: 1

Bernard Schott, Jul 20 2022

Primes whose reversal is an even integer.

			43 is a term because 43 is prime and 34 is an even number.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Intersection of A000040 and A273892.
Equals disjoint union of A045708, A045710, A045712 and A045714.
Primes whose reversal is a multiple of k: this sequence (k=2), {3} (k=3), A045711 (k=5), A087762 (k=7), {11} (k=11), A087764 (k=13), A087765 (k=17), A087766 (k=19), A087767 (k=23).

imax=142; a={}; For[i=1, i<=imax, i++, If[EvenQ[FromDigits[Reverse[IntegerDigits[Prime[i]]]]], AppendTo[a,Prime[i]]]]; a (* Stefano Spezia, Jul 20 2022 *)
Select[Prime[Range[200]],EvenQ[IntegerDigits[#][[1]]]&] (* Harvey P. Dale, May 18 2025 *)

isok(k) = isprime(k) && !(fromdigits(Vecrev(digits(k))) % 2); \\ Michel Marcus, Jul 20 2022

from sympy import isprime
def ok(n): return str(n)[0] in "2468" and isprime(n)
print([k for k in range(822) if ok(k)]) # Michael S. Branicky, Jul 25 2022

from sympy import isprime
from itertools import chain, count, islice, product
def agen(): yield from chain((2,), (t for t in (b+i for d in count(1) for b in range(2*10**d, 10*10**d, 2*10**d) for i in range(1, 10**d, 2)) if isprime(t)))
print(list(islice(agen(), 62))) # Michael S. Branicky, Jul 25 2022

A355983 Primes whose reversal is a multiple of 4.

Original entry on oeis.org

23, 29, 61, 67, 211, 233, 239, 251, 257, 271, 277, 293, 401, 409, 421, 443, 449, 461, 463, 467, 487, 613, 617, 619, 631, 653, 659, 673, 677, 691, 809, 821, 823, 827, 829, 863, 881, 883, 887, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2309, 2311, 2333, 2339, 2341, 2347, 2351

Offset: 1

Bernard Schott, Jul 22 2022

Equivalently, primes starting with 21, 23, 25, 27, 29, 40, 42, 44, 46, 48, 61, 63, 65, 67, 69, 80, 82, 84, 86, 88.

Subsequence of A355430.

			67 is a term since 67 is prime and 76 is divisible by 4.

Primes whose reversal is a multiple of k: A355430 (k=2), {3} (k=3), this sequence (k=4), A045711 (k=5), A087762 (k=7), {11} (k=11), A087764 (k=13), A087765 (k=17), A087766 (k=19), A087767 (k=23).

Select[Prime[Range[350]], Divisible[IntegerReverse[#], 4] &] (* Amiram Eldar, Jul 22 2022 *)

isok(p) = isprime(p) && !(fromdigits(Vecrev(digits(p))) % 4); \\ Michel Marcus, Jul 22 2022

A355984 Primes whose reversal is a multiple of 8.

Original entry on oeis.org

23, 61, 211, 251, 257, 293, 401, 409, 443, 449, 487, 631, 673, 677, 821, 823, 827, 829, 863, 2111, 2113, 2131, 2137, 2153, 2179, 2309, 2341, 2347, 2381, 2383, 2389, 2531, 2539, 2551, 2557, 2579, 2591, 2593, 2707, 2729, 2741, 2749, 2767, 2789, 2917, 2939, 2953, 2957

Offset: 1

Bernard Schott, Jul 25 2022

Subsequence of A355430 and of A355983.

			251 is a term since 251 is prime and 152 = 8 * 19.

Primes whose reversal is a multiple of k: A355430 (k=2), {3} (k=3), A355983 (k=4), A045711 (k=5), A087762 (k=7), this sequence (k=8), {11} (k=11), A087764 (k=13), A087765 (k=17), A087766 (k=19), A087767 (k=23)

Select[Prime[Range[500]], Divisible[IntegerReverse[#], 8] &] (* Amiram Eldar, Jul 25 2022 *)

is(n) = fromdigits(Vecrev(digits(n)))%8 == 0 \\ David A. Corneth, Jul 25 2022

More terms from David A. Corneth, Jul 25 2022

A355985 Primes whose reversal is a multiple of 16.

Original entry on oeis.org

23, 61, 211, 257, 449, 487, 821, 829, 863, 2131, 2137, 2179, 2551, 2557, 2591, 2593, 2707, 2741, 2749, 2789, 2939, 2971, 4013, 4019, 4051, 4057, 4091, 4093, 4099, 4201, 4241, 4243, 4283, 4289, 4621, 4663, 4813, 4817, 6121, 6163, 6311, 6317, 6353, 6359, 6397

Offset: 1

Bernard Schott, Jul 29 2022

			257 is a term since 257 is prime and 752 = 16 * 47.

Subsequence of A355430, A355983 and A355984.

Primes whose reversal is a multiple of k: A355430 (k=2), {3} (k=3), A355983 (k=4), A045711 (k=5), A087762 (k=7), A355984 (k=8), {11} (k=11), A087764 (k=13), this sequence (k=16), A087765 (k=17), A087766 (k=19), A087767 (k=23).

Select[Prime[Range[1000]], Divisible[IntegerReverse[#], 16] &] (* Amiram Eldar, Jul 29 2022 *)

is(n) = { fromdigits(Vecrev(digits(n)))%16==0 && isprime(n) } \\ Rémy Sigrist, Jul 29 2022

More terms from Rémy Sigrist, Jul 29 2022

A356246 Primes whose reversal is a multiple of 14.

Original entry on oeis.org

41, 89, 211, 223, 281, 293, 463, 487, 499, 691, 827, 839, 2129, 2213, 2237, 2333, 2357, 2441, 2477, 2503, 2539, 2647, 2659, 2693, 2731, 2767, 2851, 2887, 2971, 4021, 4057, 4091, 4153, 4177, 4261, 4273, 4297, 4409, 4517, 4637, 4649, 4721, 4733, 4877, 4889, 4903, 4973

Offset: 1

Bernard Schott, Jul 30 2022

Intersection of A087762 and A355430.

			281 is a term since 281 is prime and 182 = 14 * 13.

Primes whose reversal is a multiple of k: A074895 (k=1), A355430 (k=2), {3} (k=3), A355983 (k=4), A045711 (k=5), A087762 (k=7), A355984 (k=8), {11} (k=11), A087764 (k=13), this sequence (k=14), A355985 (k=16), A087765 (k=17), A087766 (k=19), A087767 (k=23).

Select[Prime[Range[666]], Divisible[IntegerReverse[#], 14] &] (* Amiram Eldar, Jul 30 2022 *)

cp's OEIS Frontend

A087762 Primes whose reversal is a multiple of 7.

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A087764 Primes whose reversal is a multiple of 13.

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A087765 Primes whose reversal is a multiple of 17.

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A087767 Primes whose reversal is a multiple of 23.

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A355430 Primes starting with an even decimal digit.

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A355983 Primes whose reversal is a multiple of 4.

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A355984 Primes whose reversal is a multiple of 8.

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A355985 Primes whose reversal is a multiple of 16.

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