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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A162999 A064509 A096221 * A120367 A072831 A072388
KEYWORD
nonn,base
AUTHOR
K. D. Bajpai, May 19 2015
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)