A214123 -id:A214123 - cp's OEIS frontend

A214124 Indices of consecutive maxima in A214123.

2, 5, 8, 17, 20, 60, 160, 228, 318, 362, 522, 1638, 1692, 1998, 2054, 3834, 5208, 21210, 62810, 152352, 170168, 424784

Offset: 1

Carl R. White, Jul 04 2012

n where A214123(n) has a larger value than any previous value in that sequence, the corresponding values can be found in A214125.

It appears that for the n in this sequence, A214123(n) is O(log^2(n)).

Cf. A214123, A214125.

A214125 Consecutive maxima in A214123.

Original entry on oeis.org

1, 2, 3, 5, 9, 11, 19, 23, 25, 29, 31, 37, 41, 43, 45, 59, 83, 107, 113, 125, 143, 165

Offset: 1

Carl R. White, Jul 04 2012

Members of A214123 which are larger than any previous value in that sequence. Indices of these values can be found in A214124.

Cf. A214123, A214124.

A379743 a(n) is the smallest prime whose digital sum in base n is n.

Original entry on oeis.org

3, 5, 7, 13, 11, 13, 29, 17, 19, 31, 23, 37, 53, 29, 31, 97, 103, 37, 191, 41, 43, 67, 47, 73, 101, 53, 109, 113, 59, 61, 311, 97, 67, 103, 71, 73, 149, 191, 79, 241, 83, 127, 173, 89, 181, 139, 283, 97, 197, 101, 103, 157, 107, 109, 331, 113, 229, 233, 709, 181, 367, 311, 127, 193, 131, 199, 269

Offset: 2

Robert Israel, Dec 31 2024

For n <= 10^5, a(n) < n^2, thus a(n) = k*n + (n-k) for some k, 1 <= k < n. Is this true for all n?

			a(5) = 13 because the prime 13 = 23_5 with 2 + 3 = 5, and no smaller prime works.

Robert Israel, Table of n, a(n) for n = 2..10000

Cf. A214123.

f:= proc(n) local k,v,x;
  for k from 1 do
    v:= convert(convert(k,base,n),`+`);
    if v > n then next fi;
    x:= n*k+(n-v);
    if isprime(x) then return x fi
 od
end proc:
map(f, [$2..100]);

a[n_]:=Module[{k=1}, While[DigitSum[Prime[k],n]!=n, k++]; Prime[k]]; Array[a,67,2] (* Stefano Spezia, Jan 04 2025 *)

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A214124 Indices of consecutive maxima in A214123.

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A214125 Consecutive maxima in A214123.

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A379743 a(n) is the smallest prime whose digital sum in base n is n.

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