A168159 Distance of the least reversible n-digit prime from 10^(n-1)

1, 1, 1, 9, 7, 49, 33, 169, 7, 7, 207, 237, 91, 313, 261, 273, 79, 49, 2901, 51, 441, 193, 9, 531, 289, 1141, 67, 909, 331, 753, 2613, 657, 49, 4459, 603, 1531, 849, 2049, 259, 649, 2119, 1483, 63, 6747, 519, 3133, 937, 1159, 1999, 6921, 2949, 613, 4137, 1977, 31

Offset

1,4

Comments

A (much) more compact form of A114018 (cf. formula). Since this sequence and A114018 refer to "reversible primes" (A007500), while A122490 seems to use "emirps" (A006567), a(n+1) differs from A122490(n) iff 10^n+1 is prime <=> a(n+1)=1 <=> A114018(n)=10^n+1.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..500

Formula

a(n)=A114018(n)-10^(n-1)

Mathematica

Table[p = NextPrime[y = 10^(n - 1)]; While[! PrimeQ[FromDigits[Reverse[IntegerDigits[p]]]], p = NextPrime[p]]; p - y, {n, 55}] (* Jayanta Basu, Aug 09 2013 *)

Prog

(PARI) for(x=1, 1e99, until( isprime(x=nextprime(x+1)) & isprime(eval(concat(vecextract(Vec(Str(x)), "-1..1")))), ); print1(x-10^ (#Str(x)-1), ", "); x=10^#Str(x)-1)
(Python)
from sympy import isprime
def c(n): return isprime(n) and isprime(int(str(n)[::-1]))
def a(n): return next(p-10**(n-1) for p in range(10**(n-1), 10**n) if c(p))
print([a(n) for n in range(1, 56)]) # Michael S. Branicky, Jun 27 2022

Crossrefs

Sequence in context: A298780 A231605 A248307 * A038297 A144622 A069242

Adjacent sequences: A168156 A168157 A168158 * A168160 A168161 A168162

Keyword

base,nonn

Author

M. F. Hasler, Nov 21 2009

Status

approved