A258084 Numbers n such that n concatenated with its reversal n' yields a prime when the rightmost digit of n and leftmost digit of n' are coalesced.

2, 3, 5, 7, 10, 13, 15, 18, 19, 31, 35, 37, 38, 72, 75, 78, 79, 91, 92, 100, 103, 105, 106, 113, 114, 124, 127, 128, 133, 138, 139, 143, 147, 154, 155, 163, 165, 166, 174, 179, 181, 184, 193, 198, 199, 301, 302, 304, 307, 308, 315, 323, 324, 335, 345, 348, 351

Offset

1,1

Comments

Alternatively, numbers n such that if n is concatenated with its reversal n', blending together the rightmost digit of n and the leftmost digit of n' yields a prime.

Leading zeros of n’ are discarded. For example, with 100, the reversal is 001; discarding its leading zeros gives 1; since the rightmost digit of 100 does not coincide with the leftmost digit 1 of n’, discard the rightmost digit of 100 - that results in the concatenated number 101, which is prime.

All the terms in this sequence will generate (probably) palindromic primes.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..5493

Example

a(6) = 13: Reversal of its digits gives 31. Concatenating 13 with 31, blending together 3's, results in 131, which is prime.
a(26) = 124: Reversal of its digits gives 421. Concatenating 124 with 421, blending together 4's, results in 12421, which is prime.

Mathematica

Select[Range[1, 1200], PrimeQ[FromDigits[Join[IntegerDigits [FromDigits [Join[Most [IntegerDigits[#]]]]], IntegerDigits[FromDigits [Reverse[IntegerDigits[#]]]]]] ] &]

Prog

(PARI) for(n=1, 200, d=digits(n); m=(10^#d)*floor(n/10); s=sum(i=1, #d, d[i]*10^(i-1)); if(isprime(m+s), print1(n, ", "))) \\ Derek Orr, Jun 22 2015

Crossrefs

Cf. A000040, A004086, A054217, A054218.

Sequence in context: A162999 A064509 A096221 * A120367 A072831 A072388

Adjacent sequences: A258081 A258082 A258083 * A258085 A258086 A258087

Keyword

nonn,base

Author

K. D. Bajpai, May 19 2015

Status

approved