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A218100
Primes generating record-sized non-pandigital power.
0
2, 3, 7, 19, 23, 103, 271, 349, 91943, 118147, 133447, 165541, 1399399, 6161527, 12740363, 12789323, 20019953, 27793541, 29536943, 92364991, 653778547, 868088981, 988438109, 1274902129
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.
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());
if(f, print1(p"^"K"="rec"\n")); p=nextprime(p+1);
next()) }
CROSSREFS
Cf. A217379.
Sequence in context: A165571 A178954 A138111 * A349622 A078373 A038878
KEYWORD
base,nonn
AUTHOR
James G. Merickel, Oct 20 2012
EXTENSIONS
a(22)-a(24) added by James G. Merickel, Nov 22 2012
STATUS
approved