A271431 Primes with at least four digits that remain prime when any two adjacent groups of two digits switch places.

1103, 1109, 1123, 1163, 1181, 1193, 1301, 1303, 1319, 1321, 1327, 1361, 1777, 1783, 1907, 1913, 1931, 1933, 1949, 1951, 1979, 1987, 1993, 1997, 2113, 2131, 2161, 2311, 2333, 2339, 2347, 2377, 2381, 2389, 2393, 2399, 2707, 2713, 2729, 2741, 2777, 2791, 2909

Offset

1,1

Comments

A 4-digit prime abcd is a member if cdab is also a prime. c can be zero.

A 5-digit prime abcde is a member if both cdabe and adebc are primes. Again c can be zero, but not (of course) a.

Links

Table of n, a(n) for n=1..43.

Prog

(PARI) eva(n) = subst(Pol(n), x, 10)
switchdigits(n, k) = my(d=digits(n), v=vector(2)); v[1]=d[k]; v[2]=d[k+1]; d[k]=d[k+2]; d[k+1]=d[k+3]; d[k+2]=v[1]; d[k+3]=v[2]; eva(d)
is(n) = my(i=0); for(k=1, #Str(n)-3, if(ispseudoprime(switchdigits(n, k)), i++)); if(i==#Str(n)-3, return(1), return(0))
forprime(p=1000, 2000, if(is(p), print1(p, ", ")))

Crossrefs

Sequence in context: A178348 A359149 A250796 * A272754 A060519 A197422

Adjacent sequences: A271428 A271429 A271430 * A271432 A271433 A271434

Keyword

nonn,base

Author

Felix Fröhlich, Apr 07 2016

Status

approved