A298643 Array A(n, k) read by antidiagonals downwards: k-th base-n non-repunit prime p such that all numbers resulting from switching any two adjacent digits in the base-n representation of p are prime, where k runs over the positive integers, i.e., the offset of k is 1.

11, 191, 2, 223, 5, 2, 227, 7, 3, 2, 2111, 17, 7, 3, 2, 3847, 31, 13, 7, 3, 2, 229631, 41, 23, 11, 5, 3, 2, 246271, 53, 29, 13, 11, 5, 3, 2, 262111, 157, 47, 17, 31, 11, 5, 3, 2, 786431, 229, 53, 19, 47, 13, 7, 5, 3, 2, 1046527, 239, 101, 23, 71, 17, 13, 7, 5

Offset: 2

Author

Felix Fröhlich, Jan 24 2018

Keywords

• nonn
• tabl
• base

Comments

Conjecture: All rows of the array are infinite.

If the above conjecture is false, then this should have keyword "tabf" rather than "tabl".

Row n is a supersequence of the base-n non-repunit absolute primes. For example, row 10 (A107845) is a supersequence of the decimal non-repunit absolute primes (A129338).

Examples

			The base-3 representation of 251 is 100022. Base-3 numbers that can be obtained by switching any two adjacent base-3 digits are 10022 and 100202. These two numbers are 89 and 263, respectively, when converted to decimal, and both 89 and 263 are prime. Since 251 is the 12th number with this property in base 3, A(3, 12) = 251.
Array starts
11, 191, 223, 227, 2111, 3847, 229631, 246271, 262111, 786431, 1046527, 1047551
2,    5,   7,  17,   31,   41,     53,    157,    229,    239,     241,     251
2,    3,   7,  13,   23,   29,     47,     53,    101,    127,     149,     151
2,    3,   7,  11,   13,   17,     19,     23,     43,    131,     281,     311
2,    3,   5,  11,   31,   47,     71,     83,    103,    107,     151,     191
2,    3,   5,  11,   13,   17,     19,     23,     29,     37,      41,      43
2,    3,   5,   7,   13,   29,     31,     41,     43,     47,      59,      61
2,    3,   5,   7,   11,   13,     17,     19,     23,     37,      43,      47
2,    3,   5,   7,   13,   17,     31,     37,     71,     73,      79,      97
2,    3,   5,   7,   13,   17,     19,     23,     29,     31,      37,      43
2,    3,   5,   7,   11,   17,     61,     67,     71,     89,     137,     163
		

Crossrefs

Cf. A107845 (row 10), A129338.

Programs

PARI

switchdigits(v, pos) = my(vt=v[pos]); v[pos]=v[pos+1]; v[pos+1]=vt; v
decimal(v, base) = my(w=[]); for(k=0, #v-1, w=concat(w, v[#v-k]*base^k)); sum(i=1, #w, w[i])
is(p, base) = my(db=digits(p, base)); if(vecmin(db)==1 && vecmax(db)==1, return(0)); for(k=1, #db-1, my(x=decimal(switchdigits(db, k), base)); if(!ispseudoprime(x), return(0))); 1
array(n, k) = for(x=2, n+1, my(i=0); forprime(p=1, , if(is(p, x), print1(p, ", "); i++); if(i==k, print(""); break)))
array(6, 10) \\ print initial 6 rows and 10 columns of array