A088884 Primes which when concatenated with their reverse and decremented by 2 yield a new prime.

3, 5, 11, 53, 107, 131, 149, 167, 179, 191, 311, 317, 389, 503, 599, 947, 971, 1049, 1061, 1097, 1187, 1223, 1259, 1427, 1439, 1523, 1571, 1583, 1697, 1721, 1787, 1811, 1871, 1913, 1931, 1949, 3089, 3119, 3191, 3209, 3299, 3449, 3617, 3671, 3677, 3761

Offset

1,1

Comments

It appears that if concat(p,reverse(p))-2 is prime, then concat(p,reverse(p))+2 is not and vice versa. This was tested for the first 60000 primes.

Conjecture: except for 3, all these primes are of the form 6*k - 1. - Davide Rotondo, Apr 29 2025

Links

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

Example

53 is a term because (i) 53 is prime and (ii) when 53 is concatenated with its reverse (35) - 2, the result (5333) is prime.

Mathematica

Select[Prime[Range[600]], PrimeQ[FromDigits[Join[IntegerDigits[#], Reverse[ IntegerDigits[ #]]]]- 2]&] (* Harvey P. Dale, Apr 06 2017 *)

Crossrefs

Cf. A067087 (concatenation of n-th prime and its reverse), A088883 (with incremented rather than decremented).

Sequence in context: A268510 A004203 A201473 * A328381 A058029 A206640

Adjacent sequences: A088881 A088882 A088883 * A088885 A088886 A088887

Keyword

base,nonn

Author

Chuck Seggelin, Oct 21 2003

Status

approved