The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A108387 Doubly-transmutable primes: primes such that simultaneously exchanging pairwise all occurrences of any two disjoint pairs of distinct digits results in a prime. 4
113719, 131797, 139177, 139397, 193937, 313979, 317179, 317399, 331937, 371719, 739391, 779173, 793711, 793931, 797131, 917173, 971713, 971933, 979313, 997391, 1111793, 3333971, 7777139, 9999317, 13973731, 31791913, 79319197, 97137379 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
By my definition of (a nontrivial) transmutable prime, each digit of each term must be capable of being an ending digit of a prime, so this sequence is a subsequence of A108387, primes p such that p's set of distinct digits is {1,3,7,9}. The repunit primes (A004022), which would otherwise trivially be (doubly-)transmutable and primes whose distinct digits are other proper subsets of {1,3,7,9} are excluded here by the two-disjoint-pair condition.
LINKS
EXAMPLE
a(0) = 113719 as this is the first prime having four distinct digits and such that all three simultaneous pairwise exchanges of all distinct digits as shown below 'transmutate' the original prime into other primes:
(1,3) and (7,9): 113719 ==> 331937 (prime),
(1,7) and (3,9): 113719 ==> 779173 (prime),
(1,9) and (3,7): 113719 ==> 997391 (prime).
MAPLE
N:= 100: # to get a(1) to a(N)
R:= NULL: count:= 0:
S[1] := [0=1, 1=3, 2=7, 3=9]:
S[2] := [0=3, 1=1, 2=9, 3=7]:
S[3] := [0=7, 1=9, 2=1, 3=3]:
S[4] := [0=9, 1=7, 2=3, 3=1]:
g:= L -> add(L[i]*10^(i-1), i=1..nops(L)):
for d from 6 while count < N do
for n from 4^d to 2*4^d-1 while count < N do
L:= convert(n, base, 4)[1..-2];
if nops(convert(L, set)) < 4 then next fi;
if andmap(isprime, [seq(g(subs(S[i], L)), i=1..4)]) then
R:= R, g(subs(S[1], L)); count:= count+1;
fi
od od:
R; # Robert Israel, Jul 27 2020
CROSSREFS
Cf. A108387, A108388 (transmutable primes), A108389 (transmutable primes with four distinct digits), A107845 (transposable-digit primes), A003459 (absolute primes).
Sequence in context: A256901 A066790 A135411 * A112009 A034633 A253118
KEYWORD
base,nonn
AUTHOR
Rick L. Shepherd, Jun 02 2005
EXTENSIONS
Offset changed by Robert Israel, Jul 27 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 16:46 EDT 2024. Contains 373432 sequences. (Running on oeis4.)