A175789 -id:A175789 - cp's OEIS frontend

A175791 Primes that become another prime under the map 1 <-> 0 (acting on the digits: A222210), cf. A171013.

13, 17, 103, 107, 109, 113, 137, 167, 173, 179, 197, 307, 317, 409, 419, 607, 617, 709, 719, 1013, 1019, 1039, 1049, 1063, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1153, 1223, 1229, 1277, 1283, 1303, 1307, 1367, 1373, 1409, 1433, 1439, 1487, 1499, 1523

Offset: 1

Zak Seidov, Sep 06 2010

			13 => 3, 17 => 7, 107 => 17, 113 => 3.

Zak Seidov, Table of n, a(n) for n = 1..20000

Cf. A171013, A171057, A175789.

Reap[Do[p=Prime[n];id=IntegerDigits[p]; id2=id/.{1->0,0->1};If[PrimeQ[fd=FromDigits[id2]]&&fd != p,Sow[p]],{n,2000}]][[2,1]];
fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 0] || MemberQ[id, 1]) && PrimeQ[ FromDigits[id /. {0 -> 1, 1 -> 0}]]]; Select[ Prime@ Range@ 250, fQ] (* Robert G. Wilson v, Sep 06 2010 *)

{my(q); forprime(p=1,599, p!=(q=A222210(p)) && isprime(q) && isprime(p) && print1(p, ", "))} \\ M. F. Hasler, Feb 13 2013

A180517 Primes that become a different prime under the mapping 0 <=> 2.

Original entry on oeis.org

23, 107, 127, 211, 223, 227, 241, 271, 283, 401, 421, 503, 523, 809, 829, 1009, 1013, 1021, 1031, 1049, 1091, 1097, 1103, 1109, 1123, 1129, 1201, 1213, 1229, 1231, 1249, 1291, 1297, 1301, 1307, 1321, 1327, 1409, 1429, 1601, 1607, 1621, 1627, 2003, 2011

Offset: 1

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Robert Price, Table of n, a(n) for n = 1..2511
Index to Primes, Primes that become a different prime under some mapping.

Cf. A171014, A175791, A180517 thru A180559, A175789, A180560, A180561.

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 0] || MemberQ[id, 2]) && PrimeQ[ FromDigits[ id /. {0 -> 2, 2 -> 0}] ]]; Select[ Prime@ Range@ 350, fQ]

A180559 Primes that become a different prime under the mapping 7 <=> 9.

Original entry on oeis.org

17, 19, 79, 97, 107, 109, 137, 139, 173, 179, 193, 197, 227, 229, 347, 349, 379, 397, 577, 599, 617, 619, 709, 727, 739, 769, 827, 829, 857, 859, 907, 929, 937, 967, 1279, 1297, 1427, 1429, 1487, 1489, 1579, 1597, 1607, 1609, 1667, 1669, 1709, 1733, 1747

Offset: 1

Zak Seidov and Robert G. Wilson v, Sep 09 2010

John Cerkan, Table of n, a(n) for n = 1..10000
Index to Primes, Primes that become a different prime under some mapping.

Cf. A171056, A175791, A180517 thru A180559, A175789, A180560, A180561.

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 7] || MemberQ[id, 9]) && PrimeQ[ FromDigits[ id /. {7 -> 9, 9 -> 7}] ]]; Select[ Prime@ Range@ 275, fQ]

A180560 The number of times the n-th prime, p, can become a different prime under any mapping of some single decimal digit <=> with some other single decimal digit.

Original entry on oeis.org

3, 3, 3, 3, 0, 9, 8, 6, 7, 5, 5, 7, 5, 8, 7, 7, 5, 4, 6, 6, 9, 7, 7, 5, 6, 4, 7, 12, 10, 6, 6, 5, 10, 9, 6, 6, 9, 9, 12, 7, 10, 6, 6, 7, 9, 3, 6, 7, 7, 3, 4, 6, 8, 6, 4, 7, 4, 6, 6, 5, 7, 5, 8, 4, 5, 7, 5, 7, 10, 6, 5, 7, 8, 3, 8, 5, 6, 8, 8, 8, 8, 7, 7, 3, 9, 6, 2, 6, 9, 7, 9, 6, 3, 7, 3, 6, 7, 6, 6, 7, 7, 5, 9, 5

Offset: 1

Zak Seidov and Robert G. Wilson v, Sep 09 2010

First occurrence of k, from 0 to 45: 5, 195, 87, 1, 18, 10, 8, 9, 7, 6, 29, 172, 28, 1275, 7666, 1279, ..., .

			2 can become either 3, 5 or 7 under the proper mapping, therefore a(1)=3.
11 cannot become any other prime regardless of the mapping, therefore a(5)=0.

Robert Price, Table of n, a(n) for n = 1..2000
Index to Primes, Primes that become a different prime under some mapping.

Cf. A175791, A180517 thru A180559, A175789, A180561.

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, s[[1]]] || MemberQ[id, s[[2]]]) && PrimeQ[ FromDigits[id /. {s[[1]] -> s[[2]], s[[2]] -> s[[1]] }] ]]; t = Sort@ Flatten@ Table[s = {j, k}; Select[ Prime@ Range@ 100, fQ], {j, 0, 8}, {k, j + 1, 9}]; Table[ Length@ Position[t, Prime@ n], {n, 100}]

from sympy import isprime, prime
def a(n):
    s = str(prime(n))
    return len(set(t for t in (s.translate({ord(c):ord(d), ord(d):ord(c)}) for c in set(s) for d in "0123456789" if d!=c) if isprime(int(t))))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Oct 31 2023

a(101)-a(104) corrected by Robert Price, Oct 31 2023

A180561 Primes that cannot become a different prime under any mapping of some single decimal digit <=> with some other single decimal digit.

Original entry on oeis.org

11, 11779, 22669, 23333, 33533, 55333, 74279, 77999, 78857, 80603, 84871, 88177, 88747, 97039, 103091, 112181, 119701, 125813, 128147, 131143, 133499, 141587, 158771, 159979, 164341, 166063, 173933, 175781, 219613, 220279, 222601, 227387, 229727, 231317, 238829

Offset: 1

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Index to Primes, Primes that become a different prime under some mapping.

Cf. A175791, A180517 thru A180559, A175789, A180560.

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, s[[1]]] || MemberQ[id, s[[2]]]) && PrimeQ[ FromDigits[id /. {s[[1]] -> s[[2]], s[[2]] -> s[[1]] }] ]]; t = Union@ Flatten@ Table[s = {j, k}; Select[ Prime@ Range@ 25000, fQ], {j, 0, 8}, {k, j + 1, 9}]; Complement[ Prime@ Range@ 25000, t]

from sympy import isprime
def m(s):
    return [s.translate({ord(c):ord(d), ord(d):ord(c)}) for c in set(s) for d in "0123456789" if d != c]
def ok(n):
    return isprime(n) and not any(isprime(int(t)) for t in m(str(n)))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Oct 31 2023

Complement of all the primes with the union of the sequences A175791, A175789, A180517 thru A180559.

a(33) and beyond from Michael S. Branicky, Oct 31 2023

A180518 Primes that become a different prime under the mapping 0 <=> 3.

Original entry on oeis.org

37, 101, 107, 109, 131, 137, 139, 307, 311, 317, 337, 347, 359, 367, 379, 389, 397, 401, 409, 431, 439, 601, 631, 709, 739, 809, 839, 907, 937, 1019, 1021, 1031, 1061, 1201, 1231, 1301, 1319, 1321, 1361, 1409, 1439, 1607, 1637, 1801, 1831, 1901, 1931, 2011

Offset: 1

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index to Primes, Primes that become a different prime under some mapping.

Cf. A171016, A175791, A180517 thru A180559, A175789, A180560, A180561.

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 0] || MemberQ[id, 3]) && PrimeQ[ FromDigits[ id /. {0 -> 3, 3 -> 0}] ]]; Select[ Prime@ Range@ 350, fQ]
dp03Q[n_]:=Module[{c=FromDigits[IntegerDigits[n]/.{0->3,3->0}]},c!=n && PrimeQ[ c]]; Select[Prime[Range[350]],dp03Q] (* Harvey P. Dale, Oct 16 2016 *)

A180519 Primes that become a different prime under the mapping 0 <=> 4.

Original entry on oeis.org

43, 47, 109, 149, 307, 347, 401, 419, 431, 443, 461, 467, 479, 601, 607, 641, 647, 907, 947, 1033, 1039, 1049, 1051, 1087, 1093, 1409, 1433, 1439, 1451, 1487, 1493, 2011, 2017, 2203, 2243, 2411, 2417, 2503, 2543, 2803, 2843, 3061, 3067, 3307, 3347, 3461

Offset: 1

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Robert Price, Table of n, a(n) for n = 1..2146
Index to Primes, Primes that become a different prime under some mapping.

Cf. A171019, A175791, A180517 thru A180559, A175789, A180560, A180561.

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 0] || MemberQ[id, 4]) && PrimeQ[ FromDigits[ id /. {0 -> 4, 4 -> 0}] ]]; Select[ Prime@ Range@ 500, fQ]

A180520 Primes that become a different prime under the mapping 0 <=> 5.

Original entry on oeis.org

53, 101, 107, 151, 157, 503, 509, 523, 541, 547, 557, 571, 701, 751, 809, 859, 1009, 1031, 1049, 1097, 1103, 1153, 1409, 1459, 1531, 1549, 1559, 1597, 1607, 1657, 1709, 1759, 1901, 1951, 2039, 2053, 2503, 2539, 2609, 2659, 2801, 2851, 2903, 2953, 3011

Offset: 1

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Robert Price, Table of n, a(n) for n = 1..2172
Index to Primes, Primes that become a different prime under some mapping.

Cf. A171023, A175791, A180517 thru A180559, A175789, A180560, A180561.

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 0] || MemberQ[id, 5]) && PrimeQ[ FromDigits[ id /. {0 -> 5, 5 -> 0}] ]]; Select[ Prime@ Range@ 500, fQ]

A180521 Primes that become a different prime under the mapping 0 <=> 6.

Original entry on oeis.org

67, 103, 107, 163, 167, 307, 367, 401, 461, 503, 509, 563, 569, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 673, 683, 701, 709, 761, 769, 907, 967, 1009, 1013, 1019, 1021, 1061, 1069, 1093, 1097, 1103, 1163, 1301, 1307, 1361, 1367, 1601, 1609, 1613

Offset: 1

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Robert Price, Table of n, a(n) for n = 1..3706
Index to Primes, Primes that become a different prime under some mapping.

Cf. A171028, A175791, A180517 thru A180559, A175789, A180560, A180561.

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 0] || MemberQ[id, 6]) && PrimeQ[ FromDigits[ id /. {0 -> 6, 6 -> 0}] ]]; Select[ Prime@ Range@ 300, fQ]

A180522 Primes that become a different prime under the mapping 0 <=> 7.

Original entry on oeis.org

73, 103, 109, 173, 179, 409, 479, 701, 709, 719, 743, 761, 773, 1021, 1033, 1303, 1373, 1721, 1733, 1801, 1871, 2011, 2029, 2053, 2089, 2203, 2273, 2711, 2729, 2753, 2789, 3019, 3061, 3079, 3301, 3371, 3709, 3719, 3761, 4021, 4051, 4073, 4093, 4099, 4201

Offset: 1

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Robert Price, Table of n, a(n) for n = 1..1956
Index to Primes, Primes that become a different prime under some mapping.

Cf. A171034, A175791, A180517 thru A180559, A175789, A180560, A180561.

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 0] || MemberQ[id, 7]) && PrimeQ[ FromDigits[ id /. {0 -> 7, 7 -> 0}] ]]; Select[ Prime@ Range@ 600, fQ]

cp's OEIS Frontend

A175791 Primes that become another prime under the map 1 <-> 0 (acting on the digits: A222210), cf. A171013.

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A180517 Primes that become a different prime under the mapping 0 <=> 2.

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A180559 Primes that become a different prime under the mapping 7 <=> 9.

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A180560 The number of times the n-th prime, p, can become a different prime under any mapping of some single decimal digit <=> with some other single decimal digit.

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A180561 Primes that cannot become a different prime under any mapping of some single decimal digit <=> with some other single decimal digit.

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A180518 Primes that become a different prime under the mapping 0 <=> 3.

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A180519 Primes that become a different prime under the mapping 0 <=> 4.

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A180520 Primes that become a different prime under the mapping 0 <=> 5.

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A180521 Primes that become a different prime under the mapping 0 <=> 6.

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