A322474 Primes that are not base-10 deletable primes (written in base 10).

11, 19, 41, 61, 89, 101, 109, 149, 151, 181, 191, 199, 211, 227, 241, 251, 257, 277, 281, 349, 389, 401, 409, 419, 421, 449, 461, 491, 499, 521, 541, 557, 577, 587, 601, 619, 641, 661, 691, 727, 757, 787, 809, 811, 821, 827, 857, 877, 881, 887, 911, 919, 941, 991, 1009, 1019, 1021, 1049, 1051, 1061

Offset

1,1

Comments

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed. Thus 2003 is in this sequence but not in A081027.

Complement of all nonprimes and A305352.

Links

Robert Price, Table of n, a(n) for n = 1..530

Mathematica

b = 10; d = {};
p = Select[Range[2, 10000], PrimeQ[#] &];
For[i = 1, i <= Length[p], i++,
c = IntegerDigits[p[[i]], b];
If[Length[c] == 1, AppendTo[d, p[[i]]]; Continue[]];
For[j = 1, j <= Length[c], j++,
t = Delete[c, j];
If[t[[1]] == 0, Continue[]];
If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]]; Complement[Table[Prime[n], {n, PrimePi[Last[d]]}], d] (* Robert Price, Dec 09 2018 *)

Crossrefs

Cf. A080608, A080603, A096235-A096246, A321657, A305352, A081027.

Sequence in context: A278799 A337508 A081027 * A084986 A034844 A092627

Adjacent sequences: A322471 A322472 A322473 * A322475 A322476 A322477

Keyword

nonn,base,easy

Author

Robert Price, Dec 09 2018

Status

approved