|
|
A323532
|
|
Numbers k such that the decimal concatenation of the numbers from 1 up to k followed by digit reversals of the numbers from (k-1) down to 1 is a prime.
|
|
1
|
|
|
|
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. 1070-71) for which only a(1)-a(2) are known.
a(1) corresponds to a memorable prime (12345678910987654321); a(4) > 10000 (if it exists).
|
|
LINKS
|
|
|
EXAMPLE
|
10 is a term because 12345678910987654321 is a prime.
2219 is a term because 1...22172218221981227122...1 is a 15534-digit 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*n-1, k, if(k<=n, Str(k), concat(apply(x->Str(x), Vecrev(digits(2*n-k))))))));
|
|
CROSSREFS
|
Cf. A173426 (similar but different concatenation scheme).
|
|
KEYWORD
|
nonn,base,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|