A145709
Number of primes among first 10^n primes that have first and last digits both equal 1.
Original entry on oeis.org
1, 6, 39, 393, 7737, 103788, 1230898, 13344414, 120133545, 1092391851
Offset: 1
a(1)=1 because among first 10^1 primes (i.e., from 2 to 29) there is just one prime with first and last digits equal 1, that is 11.
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10 'leading-trailing digits 20 N=11:C=4:Q=1 30 'print 2;3; 40 A=3:S=sqrt(N) 50 B=N\A 60 if B*A=N then 190 70 A=A+2 80 if A<=S then 50 90 R=str(N) 100 T=left(R,2):X=val(T) 110 U=right(R,1):Y=val(U) 120 if X=Y and X=1 then Aa=Aa+1 130 if X=Y and X=3 then Bb=Bb+1 140 if X=Y and X=7 then Cc=Cc+1 150 if X=Y and X=9 then Dd=Dd+1 160 C=C+1 170 'print C;N;X;Y;Aa;Bb;Cc;Dd 180 if C=10^Q then print C;N;Aa;Bb;Cc;Dd:Q=Q+1 190 N=N+2:goto 40
A145711
Number of primes p in the range 9 < p <= prime(10^n) that have most significant and least significant decimal digit both equal to 7.
Original entry on oeis.org
0, 0, 32, 264, 2103, 17891, 155956, 1379175, 12374435, 112213301
Offset: 1
a(3) = 32 because there are 32 primes in the set, from p(129)=727 to p(962)=7577.
A145710
Number of primes among first 10^n primes that have first and last digits both equal 3 (not counting the prime 3).
Original entry on oeis.org
0, 4, 32, 278, 2250, 18839, 162662, 1433999, 12811208, 115798814
Offset: 1
a(2)= 4 because among first 10^2 primes (i.e., from 2 to 541), there are 4 primes with first and last digits equal 3, that are 313, 353, 373, and 383.
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10 'leading-trailing digits 20 N=11:C=4:Q=1 30 'print 2;3; 40 A=3:S=sqrt(N) 50 B=N\A 60 if B*A=N then 190 70 A=A+2 80 if A<=S then 50 90 R=str(N) 100 T=left(R,2):X=val(T) 110 U=right(R,1):Y=val(U) 120 if X=Y and X=1 then Aa=Aa+1 130 if X=Y and X=3 then Bb=Bb+1 140 if X=Y and X=7 then Cc=Cc+1 150 if X=Y and X=9 then Dd=Dd+1 160 C=C+1 170 'print C;N;X;Y;Aa;Bb;Cc;Dd 180 if C=10^Q then print C;N;Aa;Bb;Cc;Dd:Q=Q+1 190 N=N+2:goto 40
A145712
Number of primes p in the range 9 < p <= prime(10^n) that have most significant and least significant decimal digit both equal to 9.
Original entry on oeis.org
0, 0, 2, 245, 2053, 17518, 153645, 1362970, 12244431, 111153241
Offset: 1
a(3)=2 because out of the first 1000 primes, only two have first and last digits 9, 919 and 929.
Better definition from R. J. Mathar, Aug 04 2010
Showing 1-4 of 4 results.