A073507
Number of primes == 7 (mod 10) less than 10^n.
Original entry on oeis.org
1, 6, 46, 308, 2411, 19621, 166211, 1440495, 12712314, 113764039, 1029518337, 9401997000, 86516367790
Offset: 1
a(2)=6 because there are 6 primes == 7 (mod 10) less than 10^2. They are 7, 17, 37, 47, 67 and 97.
Cf.
A006880,
A087632,
A073505,
A073506,
A073508,
A073509,
A073510,
A073511,
A073512,
A073513,
A073514,
A073515,
A073516,
A073517.
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c = 0; k = 7; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]
A073508
Number of primes == 9 (mod 10) less than 10^n.
Original entry on oeis.org
0, 5, 38, 303, 2390, 19593, 166032, 1440186, 12711333, 113761326, 1029509896, 9401974132, 86516371101
Offset: 1
a(2) = 5 because there are 5 primes == 9 (mod 10) less than 10^2. They are 19, 29, 59, 79 and 89.
Cf.
A006880,
A087633,
A073505,
A073506,
A073507,
A073509,
A073510,
A073511,
A073512,
A073513,
A073514,
A073515,
A073516,
A073517.
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c = 0; k = 9; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]
A308945
Number of totient numbers, phi(k), k <= 10^n, whose initial digit is 1.
Original entry on oeis.org
2, 20, 213, 2152, 21594, 216009, 2159776, 21595522, 215951111, 2159507603, 21595061256, 215950604593
Offset: 1
a(1)=2 as the first 10 totient numbers are {1, 1, 2, 2, 4, 2, 6, 4, 6, 4} and the occurrence of numbers with an initial 1 is 2.
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lst1={}; Do[lst=Table[0, {n, 1, 9}]; Do[++lst[[First@IntegerDigits@EulerPhi[n]]], {n, 1, 10^m}]; AppendTo[lst1, lst[[1]]], {m, 1, 7}]; lst1
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a(n) = {k=0; for(j=1, 10^n, if(digits(eulerphi(j))[1]==1, k++)); k} \\ Jinyuan Wang, Jul 04 2019
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