

A260866


Base16 representation of a(n) is the concatenation of the base16 representations of 1, 2, ..., n, n1, ..., 1.


20



0, 1, 289, 74529, 19088161, 4886709025, 1250999747361, 320255971115809, 81985529178309409, 20988295478809805601, 5373003642721911784225, 1375488932539155041567521, 352125166730061220638180129, 90144042682896272963324429089, 23076874926821455486290258903841
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OFFSET

0,3


COMMENTS

See A260343 for the bases b such that B(b) = A_b(b) = b*c + (c  b)*(1 + b*c), is prime, where A_b is the baseb sequence, as here with b=16, and c = R(b,b) = (b^n1)/(b1) is the baseb repunit of length b.


LINKS

Table of n, a(n) for n=0..14.
D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015


FORMULA

For n < b = 16, we have a(n) = A_b(n) = R(b,n)^2, where R(b,n) = (b^n1)/(b1) are the baseb repunits.


EXAMPLE

a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = (16+1)^2 = 16^2 + 2*16 + 1 = 121_16, concatenation of (1, 2, 1).
a(17) = 123456789abcdef101110fedcba987654321_16 is the concatenation of (1, 2, 3, ..., 9, a, ..., f, 10, 11, 10, f, e, ..., 1), where the middle "10, 11, 10" are the base16 representations of 16, 17, 16.


PROG

(PARI) a(n, b=16)=sum(i=1, #n=concat(vector(n*21, k, digits(min(k, n*2k), b))), n[i]*b^(#ni))


CROSSREFS

Base16 variant of A173426 (base 10) and A173427 (base 2). See A260853  A260865 for variants in other bases.
Sequence in context: A156161 A114762 A226747 * A252360 A125249 A013761
Adjacent sequences: A260863 A260864 A260865 * A260867 A260868 A260869


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Aug 01 2015


STATUS

approved



