A383816 Palindromic primes which satisfy the requirements of A380943 in at least two ways.

373, 1793971, 7933397, 374636473, 714707417, 727939727, 787333787, 790585097, 947939749, 991999199, 10253935201, 11365556311, 11932823911, 13127372131, 34390609343, 35369996353, 35381318353, 36297179263, 37018281073, 37423332473, 37773537773, 38233333283, 38914541983, 39064546093

Offset

1,1

Comments

Terms of A380943 are primes whose decimal representation is the concatenation of primes p and q such that the concatenation of q and p also forms a prime.

Links

Table of n, a(n) for n=1..24.

Example

The palindromic prime 373 meets the requirements of A380943 in two ways: the concatenation of 3 and 37 forms the prime 337, and the concatenation of 73 and 3 forms the prime 733.
Although 37673 is a palindrome where 3, 7673, and 76733 are all primes and 3767, 3, and 33767 are all primes, the palindrome is not prime and is therefore not in the sequence.

Mathematica

f[n_] := Block[{cnt = 0, id = IntegerDigits@ n, k = 1, len, p, q, qp}, len = Length@ id; While[k < len, p = Take[id, k]; q = Take[id, -len + k]; qp = FromDigits[Join[q, p]]; If[ PrimeQ@ FromDigits@ p && PrimeQ@ FromDigits@ q && PrimeQ@ qp && IntegerLength@ qp == len, cnt++]; k++]; cnt]; fQ[n_] := Reverse[idn = IntegerDigits@ n] == idn && f@ n > 1; Select[ Prime@ Range@ 3000000, fQ]

Crossrefs

Subsequence of A383810.

Cf. A000040, A002385, A105184, A380943.

Sequence in context: A208834 A171216 A108844 * A025336 A025328 A380749

Adjacent sequences: A383813 A383814 A383815 * A383817 A383818 A383819

Keyword

base,nonn

Author

James C. McMahon and Robert G. Wilson v, Jun 09 2025

Status

approved