A077345 -id:A077345 - cp's OEIS frontend

A262369 A(n,k) is the n-th prime whose decimal expansion begins with the decimal expansion of k; square array A(n,k), n>=1, k>=1, read by antidiagonals.

11, 2, 13, 3, 23, 17, 41, 31, 29, 19, 5, 43, 37, 211, 101, 61, 53, 47, 307, 223, 103, 7, 67, 59, 401, 311, 227, 107, 83, 71, 601, 503, 409, 313, 229, 109, 97, 89, 73, 607, 509, 419, 317, 233, 113, 101, 907, 809, 79, 613, 521, 421, 331, 239, 127

Offset: 1

Alois P. Heinz, Sep 20 2015

			Square array A(n,k) begins:
:  11,   2,   3,  41,   5,  61,   7,  83, ...
:  13,  23,  31,  43,  53,  67,  71,  89, ...
:  17,  29,  37,  47,  59, 601,  73, 809, ...
:  19, 211, 307, 401, 503, 607,  79, 811, ...
: 101, 223, 311, 409, 509, 613, 701, 821, ...
: 103, 227, 313, 419, 521, 617, 709, 823, ...
: 107, 229, 317, 421, 523, 619, 719, 827, ...
: 109, 233, 331, 431, 541, 631, 727, 829, ...

Alois P. Heinz, Antidiagonals n = 1..200, flattened
Index entries for primes involving decimal expansion of n

Columns k=1-9 give: A045707, A045708, A045709, A045710, A045711, A045712, A045713, A045714, A045715.
Row n=1 gives A018800.
Main diagonal gives A077345.
Cf. A077344, A262365.

u:= (h, t)-> select(isprime, [seq(h*10^t+k, k=0..10^t-1)]):
A:= proc(n, k) local l, p;
      l:= proc() [] end; p:= proc() -1 end;
      while nops(l(k))

u[h_, t_] := Select[Table[h*10^t + k, {k, 0, 10^t - 1}], PrimeQ];
A[n_, k_] := Module[{l, p}, l[] = {}; p[] = -1; While[Length[l[k]] < n, p[k] = p[k]+1; l[k] = Join[l[k], u[k, p[k]]]]; l[k][[n]]];
Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 12}] // Flatten (* Jean-François Alcover, Dec 06 2019, from Maple *)

A077344 Triangle in which n-th row contains n smallest primes beginning with n.

Original entry on oeis.org

11, 2, 23, 3, 31, 37, 41, 43, 47, 401, 5, 53, 59, 503, 509, 61, 67, 601, 607, 613, 617, 7, 71, 73, 79, 701, 709, 719, 83, 89, 809, 811, 821, 823, 827, 829, 97, 907, 911, 919, 929, 937, 941, 947, 953, 101, 103, 107, 109, 1009, 1013, 1019, 1021, 1031, 1033

Offset: 1

Amarnath Murthy, Nov 05 2002

			Triangle begins:
:  11;
:   2,  23;
:   3,  31,  37;
:  41,  43,  47, 401;
:   5,  53,  59, 503,  509;
:  61,  67, 601, 607,  613,  617;
:   7,  71,  73,  79,  701,  709,  719;
:  83,  89, 809, 811,  821,  823,  827,  829;
:  97, 907, 911, 919,  929,  937,  941,  947,  953;
: 101, 103, 107, 109, 1009, 1013, 1019, 1021, 1031, 1033;

Alois P. Heinz, Rows n = 1..200, flattened
Index entries for primes involving decimal expansion of n

Cf. A077345, A262369.

More terms from Alois P. Heinz, Sep 30 2015

A262366 a(n) is the n-th prime whose binary expansion begins with the binary expansion of n.

Original entry on oeis.org

2, 5, 13, 67, 43, 107, 127, 263, 307, 349, 373, 773, 839, 907, 991, 1063, 1109, 1201, 1277, 1321, 2713, 2819, 2963, 3119, 3229, 3371, 3517, 3691, 3779, 3943, 4051, 4217, 8461, 8719, 8963, 9241, 9497, 9767, 10039, 10303, 10613, 10799, 11159, 11317, 11657, 11923

Offset: 1

Alois P. Heinz, Sep 20 2015

Alois P. Heinz, Table of n, a(n) for n = 1..5000
Index entries for primes involving decimal expansion of n

Main diagonal of A262365.

Cf. A077345.

u:= (h, t)-> select(isprime, [seq(h*2^t+k, k=0..2^t-1)]):
A:= proc(n, k) local l, p;
      l:= proc() [] end; p:= proc() -1 end;
      while nops(l(k)) A(n$2):
seq(a(n), n=1..60);

cp's OEIS Frontend

A262369 A(n,k) is the n-th prime whose decimal expansion begins with the decimal expansion of k; square array A(n,k), n>=1, k>=1, read by antidiagonals.

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A077344 Triangle in which n-th row contains n smallest primes beginning with n.

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A262366 a(n) is the n-th prime whose binary expansion begins with the binary expansion of n.

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Maple