A101802 Primes which remain prime after operation "omit leftmost maximal digit" repeated until only one digit remains.

23, 29, 37, 43, 53, 59, 73, 79, 83, 97, 233, 239, 263, 283, 293, 379, 397, 439, 443, 463, 523, 563, 593, 599, 643, 653, 739, 743, 773, 823, 839, 853, 883, 929, 937, 953, 983, 997, 2333, 2339, 2383, 2393, 2399, 2633, 2663, 2683, 2693, 2833, 2939, 2963, 4463

Offset

1,1

Comments

The least digit of a term must be a prime, and can occur only once in the term. - Robert Israel, Dec 08 2024

Links

Robert Israel, Table of n, a(n) for n = 1..1250 (full sequence)

Example

9929 is a member because 9929, 929, 29 and 2 are all prime.

Maple

insert:= proc(L, d, pos)
  local Lp, i;
  Lp:= [op(L[1..pos]), d, op(L[pos+1..-1])];
  add(Lp[i]*10^(i-1), i=1..nops(Lp))
end proc:
extend:= proc(n) local L, dmax, jmax, d, i, S;
  L:= convert(n, base, 10);
  dmax:= max(L);
  for jmax from nops(L) by -1 do if L[jmax] = dmax then break fi od;
  S:= [seq(seq(insert(L, d, i), d=dmax+1..9), i=0..nops(L)),
      seq(insert(L, dmax, i), i=jmax..nops(L))];
  op(sort(select(isprime, S)))
end proc:
A[1]:= [2, 3, 5, 7]:
dmax:= 5: # for terms of up to dmax digits
for i from 2 to dmax do
  A[i]:= sort(map(extend, A[i-1]));
od:
map(op, [seq(A[i], i=2..dmax)]); # Robert Israel, Dec 09 2024

Crossrefs

Sequence in context: A180066 A353286 A101784 * A363074 A156983 A230456

Adjacent sequences: A101799 A101800 A101801 * A101803 A101804 A101805

Keyword

base,nonn,fini,full

Author

Zak Seidov, Jan 27 2005

Extensions

Name clarified by Robert Israel, Dec 08 2024

Status

approved