A171154 Smallest prime whose decimal expansion begins with concatenation of first n primes in descending order.

2, 3203, 5323, 75323, 11753221, 131175329, 171311753203, 19171311753229, 231917131175321, 292319171311753231, 3129231917131175327, 3731292319171311753239, 41373129231917131175321, 43413731292319171311753233, 4743413731292319171311753269, 534743413731292319171311753223

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 04 2009

Keywords

• nonn
• base

Comments

Sequence is conjectured to be infinite.

a(n) = "prime(n)...prime(1) R(n)".

R(n) for n>1: 03, 3, 3, 21, 9, 03, 29, 1, 31, 7, 39, 1, 33, 69, 23, 3, 59, 27, ...

It is conjectured that R(n)=1 for infinite many n.

Examples

			a(1) = 2 = prime(1) is the exceptional case, because no R(1).
a(2) = 3203 = prime(453) = "32 03", R(2)="03".
a(5) = 11753221 = prime(772902) = "prime(5)...prime(1) 21", R(5)=21.
		

References

• Leonard E. Dickson, History of the Theory of numbers, vol. I, Dover Publications 2005.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..298

Crossrefs

Cf. A000040, A066065, A019518, A089710, A053546.

Programs

Python

from sympy import isprime, primerange, prime
def a(n):
    if n == 1: return 2
    c = int("".join(map(str, [p for p in primerange(2, prime(n)+1)][::-1])))
    pow10 = 10
    while True:
        c *= 10
        for b in range(1, pow10, 2):
            if b%5 == 0: continue
            if isprime(c+b):
                return c+b
        pow10 *= 10
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Mar 12 2022

Extensions

a(14) and beyond from Michael S. Branicky, Mar 12 2022