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
A145713
Number of primes p in the range 9 < p <= prime(10^n) that begin and end with the same digit.
Original entry on oeis.org
1, 10, 105, 1180, 14143, 158036, 1703161, 17520558, 157563619, 1431557207
Offset: 1
The initial 1 is from the prime 11.
a(4)=1180 because to 10^4 or 10000 primes, ending in 104729=A006988(4), there are 1180 primes with equal and distinct first and last digits: 1 and 1, 3 and 3, 7 and 7 and 9 and 9.
a(6) corrected and a(7)-a(10) added by
D. S. McNeil, Aug 29 2010
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
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