A088565 Primes p such that the p-th digit in the decimal expansion of Pi is 1.

2, 41, 139, 149, 199, 239, 251, 397, 433, 439, 443, 491, 569, 599, 641, 647, 661, 787, 853, 883, 1031, 1087, 1097, 1153, 1187, 1319, 1423, 1613, 1619, 1637, 1657, 1667, 1697, 1759, 1789, 2081, 2129, 2143, 2221, 2239, 2459, 2633, 2689, 2741, 2753, 2777

Offset: 1

Author

Cino Hilliard, Nov 19 2003

Keywords

• nonn
• base

Examples

			The 1st digit 1 in Pi is in the 2nd place of the digits 3,1,4,1,5,9,..., and 2 is prime, whence a(1) = 2.  [Corrected and edited by _M. F. Hasler_, Jul 29 2024]
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Primes in A014976.

Cf. A088563, A088566 (the same for digits 0 and 2), A000796 (decimal digits of Pi).

Programs

Mathematica

Select[Flatten[Position[RealDigits[Pi,10,2800][[1]],1]],PrimeQ] (* Harvey P. Dale, May 05 2019 *)

PARI

pizeros(n,d) = { default(realprecision,5000); p = Pi; v = Vec(Str(p)); for(x=1,n, if(v[x] == Str(d) && isprime(x-1),print1(x-1",")) ) }

PARI

A088565_upto(N=3456, d=1)={localprec(N+20); [p|p<-primes([1, #N=digits(Pi\10^-N)]), N[p]==d]} \\ M. F. Hasler, Jul 29 2024