A387143 a(n) is the smallest prime p not already in the sequence such that the digit string of p is contained as a substring in the digit string of p^n.

2, 5, 251, 83, 3, 7, 73, 29, 43, 13, 11, 19, 59, 61, 23, 31, 17, 67, 37, 71, 41, 47, 53, 167, 97, 79, 131, 89, 113, 127, 101, 347, 137, 109, 193, 227, 307, 163, 173, 139, 107, 157, 233, 149, 199, 263, 191, 151, 239, 103, 179, 257, 229, 293, 379, 223, 353, 313, 269

Offset

1,1

Links

Felix Huber, Table of n, a(n) for n = 1..5000

Example

a(4) = 83 because the digit string "83" is contained as a substring in the digit string of 83^4 = 47458321 and for smaller primes (except for 5 which is already in the sequence) this is not the case.

Maple

A387143:=proc(N) # for a(1)..a(N)
    local i, j, k, p, q, v;
    v:=Vector(N);
    j:=0;
    for i while j<N do
        p:=ithprime(i);
        q:=convert(p, 'base', 10);
        for k to N do
            if v[k]=0 and verify(q, convert(p^k, 'base', 10), 'sublist') then
                v[k]:=p;
                j:=j+1;
                break
            fi
        od
    od;
    return op(convert(v, list))
end proc;
A387143(59);

Mathematica

s={}; Do[p=2; While[SequenceCount[IntegerDigits[p^n], IntegerDigits[p]]==0||MemberQ[s, p], p=NextPrime[p]]; AppendTo[s, p], {n, 59}]; s (* James C. McMahon, Sep 29 2025 *)

Prog

(PARI) lista(nn) = my(va = vector(nn), vsa = []); for (n=1, nn, my(p=2); while(vecsearch(vsa, p) || #strsplit(Str(p^n), Str(p)) < 2, p = nextprime(p+1)); va[n] = p; vsa = vecsort(Vec(va, n)); ); va; \\ Michel Marcus, Sep 23 2025

Crossrefs

Cf. A052073, A052075, A054260, A062584, A387142.

Sequence in context: A137068 A137066 A175977 * A367673 A121270 A085603

Adjacent sequences: A387140 A387141 A387142 * A387144 A387145 A387146

Keyword

nonn,base

Author

Felix Huber, Sep 22 2025

Status

approved