A171032 -id:A171032

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A180547

Primes that become a different prime under the mapping 4 <=> 6.

+10
1

41, 47, 61, 67, 347, 367, 401, 419, 431, 461, 463, 467, 491, 601, 619, 631, 641, 643, 647, 691, 947, 967, 1049, 1069, 1409, 1427, 1447, 1493, 1499, 1609, 1627, 1667, 1693, 1699, 1847, 1867, 2141, 2161, 2417, 2459, 2467, 2477, 2617, 2647, 2659, 2677, 3041

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

Index to Primes, Primes that become a different prime under some mapping.

MATHEMATICA

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, 4] || MemberQ[id, 6]) && PrimeQ[ FromDigits[ id /. {4 -> 6, 6 -> 4}] ]]; Select[ Prime@ Range@ 440, fQ]

dpQ[n_]:=(DigitCount[n, 10, 4]>0 || DigitCount[n, 10, 6]>0)&&PrimeQ[ FromDigits[ IntegerDigits[n]/.{4->a, 6->b}/.{a->6, b->4}]]; Select[ Prime[ Range[500]], dpQ](* Harvey P. Dale, Feb 28 2022 *)

CROSSREFS

Cf. A171032, A175791, A180517 thru A180559, A175789, A180560, A180561.

KEYWORD

base,nonn

AUTHOR

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

STATUS

approved

A222241

In the number n, replace all (decimal) digits '4' with '6' and vice versa.

+10
1

0, 1, 2, 3, 6, 5, 4, 7, 8, 9, 10, 11, 12, 13, 16, 15, 14, 17, 18, 19, 20, 21, 22, 23, 26, 25, 24, 27, 28, 29, 30, 31, 32, 33, 36, 35, 34, 37, 38, 39, 60, 61, 62, 63, 66, 65, 64, 67, 68, 69, 50, 51, 52, 53, 56, 55, 54, 57, 58, 59, 40, 41, 42, 43, 46, 45, 44, 47, 48, 49, 70, 71, 72, 73, 76, 75

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

The map which is applied to primes in A171032.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

MATHEMATICA

a[n_]:= IntegerDigits[n]/.{4->6, 6->4} // FromDigits; Table[a[n], {n, 0, 80}] (* Vincenzo Librandi, Jul 31 2013 *)

PROG

(PARI) A222241(n, d=[0, 1, 2, 3, 6, 5, 4, 7, 8, 9])={sum(i=1, #n=digits(n), d[n[i]+1]*10^(#n-i), !n*d[1])} \\ N.B.: digits(0)=[] in PARI (v.2.6)

CROSSREFS

Cf. A222210-A222254; A171013-A171016, A175770, A171018-A171057.

KEYWORD

nonn,base,easy

AUTHOR

M. F. Hasler, Feb 13 2013

STATUS

approved

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