

A323532


Numbers k such that the decimal concatenation of the numbers from 1 up to k followed by digit reversals of the numbers from (k1) down to 1 is a prime.


0




OFFSET

1,1


COMMENTS

The definition is related to the sequence discussed by N. J. A. Sloane (in Notices of the AMS (2018), Vol. 65, No. 9, pp. 107071) for which only a(1)a(2) are known.
a(1) corresponds to a memorable prime (12345678910987654321); a(4) > 10000 (if it exists).


LINKS

Table of n, a(n) for n=1..3.
N. J. A. Sloane, The OnLine Encyclopedia of Integer Sequences, Notices, Amer. Math. Soc., 65 (No. 9, Oct. 2018), 10621074.


EXAMPLE

10 is a term because 12345678910987654321 is a prime.
2219 is a term because 1...22172218221981227122...1 is a 15534digit probable prime (where 8122 following 2219 corresponds to the digit reversal of 2218, 7122 to that of 2217, etc. down to 1).


MATHEMATICA

a[n_]:=Block[{cn=Drop[FoldList[Append, {}, ToString/@Range@n], 2]}, ParallelMap[If[PrimeQ[FromDigits@@{#<>Reverse@StringReverse@Most@#}], Length@#, Nothing]&, cn]]; a[2300]


PROG

(PARI) f(n) = eval(concat(vector(2*n1, k, if(k<=n, Str(k), concat(apply(x>Str(x), Vecrev(digits(2*nk))))))));
isok(n) = ispseudoprime(f(n)); \\ Michel Marcus, Jan 20 2019


CROSSREFS

Cf. A173426 (similar but different concatenation scheme).
Sequence in context: A212925 A322654 A337342 * A273032 A185277 A006441
Adjacent sequences: A323529 A323530 A323531 * A323533 A323534 A323535


KEYWORD

nonn,base,more


AUTHOR

Mikk Heidemaa, Jan 17 2019


STATUS

approved



