A218100 - OEIS

A218100

Primes generating record-sized non-pandigital power.

2, 3, 7, 19, 23, 103, 271, 349, 91943, 118147, 133447, 165541, 1399399, 6161527, 12740363, 12789323, 20019953, 27793541, 29536943, 92364991, 653778547, 868088981, 988438109, 1274902129

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OFFSET

1,1

COMMENTS

This is computed as in the comments in A217379, but limited to prime values. The same rationale for declaring that missed records are extremely unlikely holds, but always with the caveat that astronomically rare events do occur. The power for a(25), having 219 digits, is a full 30 digits longer than that for a(24). The sequence of exponents is 168, 106, 61, 44, 50, 42, 36, 39, 20, 21, 21, 27, 23, 21, 21, 21, 22, 23, 23, 22, 20, 20, 21 and 24.

LINKS

Table of n, a(n) for n=1..24.

EXAMPLE

The PARI program below is initiated with the well-known value 2^29 which has one copy of each digit save one. Otherwise, see A217379 for examples that might reasonably appear here.

PROG

(PARI)

{ rec=2^29; p=2;

while(1,

k=ceil(log(rec)/log(p)); f=0; n=p^k;

while(n<10^399,

m=n; v=vectorsmall(10); c=9;

while(m,

d=m%10; if(v[d+1]==0, if(c, c--; v[d+1]=1, break())); m\=10;

next());

if(m==0, K=k; f=1; rec=n); k++; n*=p;

next());