A086204 Decimal equivalents of strings in A086884.

2, 2, 47, 151, 4001, 4001, 100207, 41532851, 447045215857, 282607273285049, 5678228814363947

Offset

2,1

Links

Table of n, a(n) for n=2..12.

Mersenneforum.org, Multibase primes

Example

a(5) = 10010111 because 10010111 (base 2) = 151, 10010111 (base 3) = 2281, 10010111 (base 4) = 16661 and 10010111 (base 5) = 78781 are all prime and 10010111 is the smallest such string.

Mathematica

a[n_] := (While[b = FromDigits[ IntegerDigits[k, 2]]; Union[ PrimeQ[ Table[ FromDigits[ IntegerDigits[b], i], {i, 2, n}]]] != {True}, k++ ]; b); k = 1; Do[ Print[ a[n]], {n, 2, 10}]

Prog

(Python)
from sympy import isprime
def conv(s, b): return sum(b**k for k, bk in enumerate(s[::-1]) if bk=='1')
def ok(s, n): return all(isprime(conv(s, b)) for b in range(2, n+1))
def a(n):
    if n < 4: return 2
    k = 3
    while not ok(bin(k)[2:], n): k += 2
    return int(bin(k)[2:], 2)
print([a(n) for n in range(2, 9)]) # Michael S. Branicky, Oct 10 2021

Crossrefs

Cf. A086884.

Sequence in context: A303538 A222661 A015167 * A318085 A345267 A316090

Adjacent sequences: A086201 A086202 A086203 * A086205 A086206 A086207

Keyword

nonn,base,more

Author

Richard FitzHugh (fitzhughrichard(AT)hotmail.com), Aug 22 2003

Extensions

Edited by Robert G. Wilson v, Aug 24 2003

Two more terms added by James G. Merickel, Feb 15 2010

One more term added by Andreas Höglund, Oct 17 2022 (found by Jim Viebke)

Status

approved