A213653 Least semiprime whose digital sum is n, or 0 if no such integer exists.

0, 10, 10001, 21, 4, 14, 6, 25, 26, 9, 46, 38, 39, 49, 77, 69, 169, 278, 0, 289, 299, 489, 589, 689, 699, 799, 899, 0, 2899, 3899, 4989, 5899, 5999, 6999, 7999, 9899, 0, 19999, 29999, 48999, 58999, 68999, 69999, 88999, 99899, 0, 299899, 398999, 589989

Offset: 0

Author

Robert G. Wilson v, Jun 17 2012

Keywords

• easy
• base
• nonn

Comments

a(9k) = 0 for all k>1.

I conjecture that all terms > 278, except for 10001, end in the digit "9". What is the next term a(n) > 69 violating monotony, i.e., such that a(n) < a(n-1)? M. F. Hasler, Jun 17 2012

a(88) = 7999999999 < a(87) = 8899899999. - Alois P. Heinz, Jun 17 2012

a(76) = 499999999 < a(75) = 597999999. - Donovan Johnson, Jun 18 2012

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400 (first 101 terms from Donovan Johnson)

Programs

Mathematica

semiPrimeQ[n_] := PrimeOmega[n] == 2; t = Table[0, {100}]; k = 1; While[k < 10^7, If[ semiPrimeQ@ k, s = Plus @@ IntegerDigits@ k; If[s < 101 && t[[s]] == 0, t[[s]] = k; Print[{s, k}]]]; k++]

PARI

A213653(n)={ n%9 || n==9 || return; forstep( a=A051885(n),9e9,9, bigomega(a)==2 || next; A007953(a)==n & return(a))} \\ - M. F. Hasler, Jun 17 2012

Extensions

a(0)-a(62) double-checked with given PARI code by M. F. Hasler, Jun 17 2012