A239196 A variant of primeval numbers A072857 where primes are counted with repetition as in A075053, not as in A039993.

1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1136, 1139, 1237, 1337, 1379, 10013, 10039, 10079, 10133, 10136, 10139, 10379, 12379, 13679, 100136, 100139, 100379, 101237, 102347, 102379, 103679

Offset

1,2

Comments

Coincides with A072857 up to a(10) = 1079, but then this sequence lists two "intermediate" records 1136, 1139, before a(13) = 1237 = A072857(11).

"With repetition" means that primes are counted several times if they are obtained from different (not distinct) digits (e.g., 13 is obtained twice from 113), but not if they are obtained as different permutations of the same digits (e.g., p=11 is *not* counted twice even though it results as identical permutation and transposition (2,1) from the digits [1,1]).

The initial a(1)=1 has been chosen for consistency with A072857, it could be argued that it should not be there or listed as a(0).

See A239197 for the record values A075053(a(n)) reached for these numbers which are the indices of the records in A075053.

Links

Table of n, a(n) for n=1..31.

Prog

(PARI) m=-1; for(k=1, 9e9, A075053(k)>m&&print1(k", ")+m=A075053(k)) \\ Not very efficient; from 199, 1999, 19999 etc one could jump to the next larger power of 10. - M. F. Hasler, Mar 12 2014

Crossrefs

Sequence in context: A265775 A291205 A005113 * A072857 A119535 A210849

Adjacent sequences: A239193 A239194 A239195 * A239197 A239198 A239199

Keyword

nonn,base,more

Author

M. F. Hasler, Mar 12 2014

Status

approved