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

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());
if(f, print1(p"^"K"="rec"\n")); p=nextprime(p+1);
next()) }

Crossrefs

Cf. A217379.

Sequence in context: A165571 A178954 A138111 * A349622 A078373 A038878

Adjacent sequences: A218097 A218098 A218099 * A218101 A218102 A218103

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