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A244441 a(n) is the smallest prime p such that p has at least one digit greater than 1 and all the n numbers ds(p), ds(ds(p)), ..., ds(ds(...(ds(p))...)) are primes. The function ds is defined in the comment lines. 0
2, 31, 2621, 9941, 5599921, 5599921, 5219088341 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
ds(m) is the number that is obtained from m by replacing each positive digit i to sigma(i) and replacing zero by zero itself.
Example: ds(19)=1.13=113, ds(1028)=1.0.3.15=10315.
1. If all digits of m are less than 2 then ds(m)=m. So for
primes p with digits less than 2 (terms of the sequence A020449) p=ds(p)=ds(ds(p))=ds(ds(ds(p)))= ... .
2. For n>1, a(n) is of the form 10k+1.
3. If o, i, s and t are respectively number of zeros, number of ones, number of digits greater than 1 and number of composite digits greater than 4 in decimal expansion of m also o', i', s' and t' are the same for ds(m) then o'=o, i'=i+t and s'=s.
Example: m=1021041629839
ds(m)=1.0.3.1.0.7.1.12.3.13.15.4.13=10310711231315413
=> {o, i, s, t}={2, 3, 8, 4} and {o', i', s'}={o, i+t, s}= {2, 7, 8}.
LINKS
EXAMPLE
a(3)=2621 because the three numbers:
1. ds(2621)=3.12.3.1=31231
2. ds(ds(2621))=4.1.3.41=41341
3. ds(ds(ds(2621)))=7.1.4.71=71471
are all primes and 2621 is the smallest prime with this property.
CROSSREFS
Sequence in context: A197320 A239332 A350940 * A004072 A113030 A247873
KEYWORD
nonn,base,hard,more
AUTHOR
STATUS
approved

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Last modified July 22 12:12 EDT 2024. Contains 374499 sequences. (Running on oeis4.)