A173189 -id:A173189 - cp's OEIS frontend

A227949 Primes obtained by concatenating decremented numbers starting at a power of 10.

109, 10099, 10987, 1000999, 100999897, 10000099999, 1000000999999, 1000999998997, 100000009999999, 10000999999989997, 1000000000999999999, 100999897969594939291, 1000999998997996995994993, 100000000000009999999999999, 10000000000000000000000000099999999999999999999999999

Offset: 1

James G. Merickel, Aug 01 2013

			Since the concatenation of 10 and 9 produces the prime 109, the number 109 is in the sequence.
Since the concatenation of 100 and 99 produces the prime 10099, the number 10099 is in the sequence.
The concatenation of 100, 99, 98 does not produce a prime, hence 1009998 is not in the sequence.

Robert Israel, Table of n, a(n) for n = 1..26

Cf. A173189, A096594, A172998.

Cf. A227950, A227951.

N:= 100: # for terms of up to N digits:
S:= NULL:
for m from 1 to N/2 do
  for k from 1 by 2 to 10^m do
    x:= parse(cat(seq(i,i=10^m .. 10^m - k, -1)));
    if length(x) > N then break fi;
    if isprime(x) then S:= S, x;  fi
od od:
sort([S]); # Robert Israel, Jan 23 2024

A227949(n) begins with 10^[(A227950(n)-1)/A227951(n)].

A227775 Smallest prime that is a concatenation in base n of two or more successive numbers beginning with a power of n (including n^0=1).

Original entry on oeis.org

11, 5, 1298074219469410275663133932519427, 7, 223, 131870666077, 83, 11

Offset: 2

James G. Merickel, Jul 30 2013

Terms computed by expanding the print for the program at A173189 (to include the variable r).

a(10) consists of 10^13 followed by 10^13+k, k=1 to 9 in order (140 digits), and then follow 13 and 1741. a(13) has 258 decimal digits, and then 227, 17, 320255973501901, 19 and 5851 follow before a P209 arises for n=19 (n=31 produces the next prime that would not fit a mainline sequence here, at 467 digits; and the number for n=67, the concatenation in that base of 67^19 through 67^19+525, is a whopping 19209 decimal digits). Terms through at least n=78 may be found in a reasonable time using the program (and sped up by a small factor if it is modified to only search for r). a(79) is very large, however, and has a high heuristic probability of being beyond current computational means, as candidates having the right number of numbers concatenated to avoid being divisible by a small prime arise only about once every 11 orders of magnitude.

			11 is the decimal representation of the value for n=2 as the concatenation 10 followed by 11 in binary, with the only smaller concatenation of type (110, 6 in decimal) composite.

Prime Curios!, 10000...00009 (140-digits)

Cf. A173189.

a(p-2) = p if p is an odd prime.

cp's OEIS Frontend

A227949 Primes obtained by concatenating decremented numbers starting at a power of 10.

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